Can I get a small, nice quality book made out of my own prints that I made like the books that you can get at a lot of photo services today, like WalMart and Shutterfly and Apple? Without breaking the bank, that is.
Depends on how well built the bank is... :-)
There are several online companies that will publish small runs for reasonable prices. I know a couple people who have used these services (specifically one in China, but at the moment I can't remember the name). I've talked to them about it, have some mild interest, but have never proceeded beyond a cursory look. The only one I can think of off hand is lulu.com. I'm not recommending that specific company, but it will certainly give you an idea of what can be done.
Another option may or may not be equally interesting, which is to literally do both printing and binding yourself. I don't know that it is possible to do a high quality book binding, but for a few hundred dollars a machine that does a plastic spiral binding might be an option. Higher priced machines can do larger books and are easier for larger quantities. If punched holes and plastic spiral, wire loop, or plastic comb bindings are acceptable, and particularly if production runs are very small, this might be an acceptable way to produce suitable books.