Upvote:5
Yes, you can surrender your green card, and yes, you can apply for a multiple-entry tourist visa. You would file Form I-407, Record of Abandonment of Lawful Permanent Resident Status, and then you would apply for your visa using the online DS-160. You'll also need to schedule an interview appointment at a US embassy or consulate.
You may want to consider the tax implications of doing this; questions about that would be off topic here, but you could ask at Expatriates or Personal Finance and Money.