I think that to meet people you need to choose your area and accommodation well - while there are tourists all over the place, a good starting point would be the popular areas like Sukhumvit and Silom - not only a lot of bars and pubs where you could meet people and chat over a few drinks, but generally a lot of entertainment in those areas.

Perhaps a better chance of meeting people your own age in accomm. where there are likely to be a lot of younger people - guest houses, lower priced accomm. rather than upmarket hotels or apartments which tend to atract couples, older travellers, business travellers and families.
That's been my experience anyway.

Some people might suggest Khao San Rd. which is commonly known as the backpacker area of Bangkok - lots of guesthouses and cheaper accomm. and also the starting point for a lot of backpacker tours. This would be one way of meeting up with people with similar interests.

On one of my first trips to Thailand I was alone and in a fairly isolated beach resort - no problem for me as I needed a bit of peace and quiet, but the place was full of older couples, some families and tour groups of middle-aged people from Norway, Sweden and other parts of Europe as is often the case at larger or mid-range hotels in Thailand's beach areas. Some of these people invited me to join them for dinner or drinks when they saw me sitting alone.
But this type of place wouldn't suit you at all - too quiet.
Stick with the low - mid priced places in popular, busy areas and I think you'll meet more people to do things with or travel with.