What areas to avoid in Brussels after the recent terrorism events

The only area that would be considered "hot" these days in Bruxelles proper is around Molenbeek-Sint-Jans.

Otherwise, Bruxelles is as safe as any other major cities in the world.

ISIS has sent about 400 highly skilled terrorists to Western Europe in recent weeks. This means that large scale attacks similar to e.g. the 2008 Mumbai attacks are possible anywhere in mainland Western Europe. Britain is probably safer because it's more difficult to bring explosives and guns into that country. Within mainland Europe, it's relatively easy to transport guns, ammunition and explosives. These are typically obtained in the Balkan region and then transported unnoticed across internal borders to the destination, e.g. Brussels and Paris in case of the recent attacks.

To kill as many people as possible, a terrorist will try to explode his bomb in a confined place where there are many people. So, you can reduce your risk by avoiding such places. Such places with few exits may also be attacked by gunmen who block all exists and start to shoot people. The safest places to visit would be locations in smaller towns or rural areas. So, you could e.g. consider visiting Brugge instead of Brussels. While there you'll also find the same sort of potentially dangerous locations, a terrorist will probably not strike in low profile locations.

I am the founder of the website CitySafe which aims to assess the crime and safety levels of large cities and countries worldwide (it’s still work-in-progress, but so far I have done c. 40 cities and countries).

For my answer, I am referring to the page about safety in Belgium and Brussels (including a crime map). (FYI, Citysafe’s rating algorithm has assessed a safety level of 70% (100% being the safest) to Belgium, and 60% to Brussels.

Brussels is a safe city for tourists. The main risk is petty crime and pickpocketing in the subway or at the train stations (Bruxelles Midi, Bruxelles North and Bruxelles Central station). There is a high terrorist threat going on in the country; so it is best to avoid very crowded areas and public demonstrations.

The following neighborhoods are best avoided for tourists especially during the night : Anneessens, Anderlecht, Chaarbeek, Brussels North, St-Josse, Marollen and Molenbeek. To view those neighborhoods on a map, check the page: http://www.city-safe.com/europe/belgium/

Personally, if it is feasible and you won't lose out financially, I would delay a trip to Brussels for at least a month or so, more for the stress and inconvenience of closed public transit, the fact if you are flying you will have to travel to a distant airport, probably in a neighboring country (Schiphol I would reckon) and take land transportation the rest of the way, and the extra security than any real terrorist threat.

If you were flying in, as I said, your flight will almost definitely be cancelled and your airline will offer a full refund or possibly offer an alternative airport and land transport to Brussels. So you have the opportunity to decide then if you want to cancel your trip. Likewise with hotels, I expect most will be willing to have you cancel your reservation at no cost, even if it is normally not possible, because of the exceptional circumstances. Other costs, well it depends on what you have paid for, you would have to see on a case by case basis. Insurance will be no help whatsoever, the vast majority of policies specifically exclude anything caused by terrorism.

Perhaps consider visiting another European city this time, and save Brussels once things have calmed down a little.

There is not one particular area to avoid.

I would just recommend you to follow the Crisiscentrum, @CrisiscenterBE and local media, to be aware of advises, special measures taken by local authorities and alert levels.

Because of events a few days after the posting of the question, I'm adding a second answer. On 22 March 2016, there were several attacks on Brussels. At the moment confirmed are a bombing of Brussels Airport and an explosion in or near Maalbeek metro station.

The points below are partly speculation, but based on the experience of someone working in Brussels. They might get outdated quickly. I've made the post a community wiki, so feel free to edit.

From the point of view of a traveler:

• The chances that you will be the victim of an attack are minimal. I wouldn't worry about that. And I am at 300 meters from where the metro bombing took place. Watch out for traffic instead of terrorists if you want to stay safe.
• The airport is closed and judging from the pictures that circulate now it looks like it might be a while. Talk is an entirely destroyed departure hall. I'm supposed to fly from Brussels Airport on Friday. No idea if that will be possible.
• The metro is closed at the moment. My estimation (based on experience from what happened after the Paris attacks and some guessing) is that it will not operate for a while. I'm counting on a week or more.The metro is running on a limited number of stretches (lines 1 and 5) on both sides of Maalbeek, but with a very limited number of stops. The vast majority of metro stations is closed.
• The main Brussels train stations (South, Central, North and Schuman) are closed at the moment. This is a problem because I would like to take the train home tonight. My estimation is that trains will operate again as usual soon. I would be surprised if there are still no trains tomorrow.Trains started operating in the late afternoon on the day of the attacks. Queues are enormous at the moment because everybody entering the stations gets a pat down and luggage has to be opened. Source: I just went through it. You can expect things to be close to normal from tomorrow (=Wed 23 March) on, mainly depending on the security measures in place.
• At the moment there is no public transportation in Brussels. All trams and buses are stopped. I expect this to get back to normal soon (like the trains or sooner). Buses and trams start operating. Expect more or less normal service the day after the attacks. Many underground tram stations remain closed until further notice.

The main points for tourists traveling to, from and in Brussels:

• Security services will be on very high alert. Expect them to be out in full force. Avoid making any jokes with them.
• I expect lots of luggage and id checks in the following days. Provide ample time if you would like to travel. I wouldn't be surprised by luggage scans at train stations, especially for international trains, and to enter the airport building once the airport reopens. Traveling with a minimum of luggage might help.
• I expect the same, but to a somewhat lesser degree in other Belgian cities and in cities in France, Germany and the Netherlands.
• Keep an eye on the news to see what is operating and what is not.

What if you would like to travel to or from Brussels?

• Driving a car is possible. There are a few long distance buses, mainly to/from Amsterdam and Paris. Check the websites of Eurolines, Ouibus and Megabus. At the moment I don't know if they are operating, but expect that they will be the first to get back to normal.They are riding.
• At the moment there are no flights to or from Brussels. It is unclear when flights will resume. If you have a reservation for a flight, follow the news to see when the airport will open. Contact your airline for updates and ask what they offer. They might be able to get you to or from a nearby city. If you are looking for a new booking try the airports of Charleroi, Amsterdam, Frankfurt, Paris and Dusseldorf and to a lesser extent (because there are not many destinations) Eindhoven, Antwerp, Ostend, Liege, Maastricht and Lille. Low cost operators that are also active on the regional airports (Ostend, Charleroi, Antwerp and Liege) have relocated everything there. This is mainly Ryanair and JetAir. Among other airlines I see lots and lots of cancelled flights.
• Brussels is usually well connected by high speed trains to Paris, London, Amsterdam and Cologne. As long as the rail stations are closed those can not operate. I expect them to resume service soon, but with very high security measures.Thalys, the operator of most HST, announced that with a few exceptions their trains will ride the day after the attacks. They announce extra security measures. If you come early enough to the station you should be good. The other operators will probably similar. Check the websites of Eurostar (to London) and NMBS Europe. Alternatively, you might take local trains to cross the border. That is possible, but slow.