There are many places to see, things to do and experience in Thailand (not just in bangkok!)
These links might help =>
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Backpackers Area (I think) would be around Khao San Road and Rambuttri Alley. Its a place where you get to meet and party with travelers from all around the world. You can find lots of cheap/decent accommodations there like from 500 Baht a night but you can get a room for as little as 300 baht a night. Food and beverages may be expensive in Khao San Road (especially those international bars or fastfood chains) but you can still find some cheap/affordable ones around Bangkok. Food can cost as little as 40 Baht a meal but budget for at least 300 baht a day on food- western resturants 500 - 1000 Baht a meal.
down south, Phuket and Samui are really nice places to go but also expensive
you can fly to Krabi or Chiang mai instead (try airasia)