Upvote:5
It should be easy to find a place to exchange either euros or pounds to local currency both in Czechia and Hungary.
Dollars will work too, but since you need euros and pounds anyway in Austria and the UK, it would just inflate your exchange fee budget for no good reason to do a separate peso-to-dollar transaction.
You may be able to get touristy places in Prague to accept euros, but expect to get an abysmal rate for them compared to going to an actual foreign-exchange counter. Pounds or dollars will be worse.
In any case, don't overthink it. If you have only a few days in the country, the loss you make by having local cash left in pocket when you leave will far outweigh whichever small differences in exchange rate margins there are between pounds and euros anyway.