I've found myself in a similar situation, I think. I'd like to do some travelling but I find myself getting hung up on money and overall I just don't know what I would spend my time doing. What did you do once you arrived in a town or city? I really would love to have an idea of what one would do in a situation like that.
You can just .... wander around. That's the beauty of traveling alone. There is no mutually agreed upon agenda - just do whatever you want. Go from place to place for as long as you feel like. Decide last minute where you want to go next. This may or may not appeal to you depending on your personality, but I have found it to be exhilarating. You pick up and leave travel companions along the way. I spent about 4 months in SE Asia just wandering from place to place - even ended up going to some countries I didn't originally intend. :-)
I've also noticed that people are a lot more likely to come up and start a spontaneous conversation with me when I'm not already part of a group of people. I don't know exactly why that is.....
Regarding the money constraint - if you wanted to go pretty cheap you can fairly easily travel in SE Asia for less than $1000 per month. Hostels are cheap. The best food is also the cheapest. Lots of cool things to do for free or very little money.
It sounds silly, but I really do. I toured ireland by bike with a friend of mine (so I wasn't alone) and there were a few times we split up and went off onto different paths, then would meet up later. I liked seeing things, meeting other people, and finding little used bookstores to sell of my previous book and buy another. Then I'd find a little cafe or restaurant and read a little.
I guess that's mostly just to say that you can really do whatever you enjoy normally for fun; sometimes it just feels better doing it in a different location, around a different culture. At first I thought "man, I wasted my money flying out here to read" but then I realized that I really liked it, and so, who cares? It was great.
I agree with the sibling post, also. I spent about a month in Thailand on a grand or so. We went all over the place. Chiang Mai was my favorite area, personally. Lots of culture, and lots to see all over, though.
I think a lot of people experience a strange sort of complementary relationship between travelling and reading. Perhaps it's something to do with the notion of exploring new territory, both physically and imaginatively. This might be why you see lots of "shared bookshelves" in hostels around the world.
You might be interested in BookCrossing.com. You write a note inside a book and leave it in another country, and it's encouraged to read the book, and then take it somewhere else, and keep track of its progress on the website. I'm not sure how successful it is in practice generally, though. I left a book once in Ho Chi Minh city and it got as far as Bangkok, but I don't know where it is now.
What do you enjoy doing? Treking, art, history? Go somewhere that has something that interests you.
I always used to take a Lonely Planet guide, and look for a cheapish hostel recommended there. There will usually be a few people in similar situations. Hang about in the common room (don't use a laptop, or mobile phone), and speak to people. Ask people if they fancy sharing a beer. They will have things that they have seen, and have loads of recommendations for you. If that doesn't work out, book on a group tour.
Its pretty easy to meet people if you put in the tiniest bit of effort.
When I arrived in a new city and wanted socialization, I'd chat with the people staying in the hostel; with few exceptions, other guests were very pleasant and open to meeting new people. If I wasn't in the mood for chatting, I'd just wander around the city, usually ending up at a local bar where a beer or two helped me get over any shyness about approaching people. If you are open to new experiences, they'll find you.
