Young people like you travelling on a budget would in far the most ways go staying in Khaosan Road in Bangkok while being there where there are hundreds of young westeners like yourselves, fairly cheap accomodations, lots of shops and bars where you might find other travel companions.

A trip to Chiang Mai in northern Thailand for a couple of days is also recommendable. For beaches you have to go to the southern part of Thailand where there are sooo many beautiful beaches and/or islands worth a visit, and I wouldn't know which one to recommend. Personally I'm living in Kanchanaburi 125 km west of Bangkok, which is a nice medium size city mainly famous for the World War II story about The Bridge Over the River Kwai and The Death Railway, but has other nice places to go. But I'm sure other people have other suggestions to consider.