I strongly recommend the Michigan Tech Math REU, with some reservations.
The director of the REU, Anant Godbole is a wonderful guy who cares a lot about the REU. He's fun, easy-going, funky, excited about you, your work, the REU, Houghton, etc. If nothing else, he is a reason to attend the program.
The math you do is fun. Basically, REUs in discrete math (combinatorics, etc.) are good for doing real research, since you don't need much, if any, technical background to answer some interesting questions in these fields. What tools you will need will be presented to you by Anant. Thus, you can have fun, make some contribution to math, and have something to publish. On publishing: Anant wants everyone to get something publishable out of the summer. Half the papers he writes are co-authored with REU participants (and he has an Erdos number of two ;-). If you want to publish something, this is a great REU for it.
In the middle of the program, the REU goes to a conference; my year (1998) we went to Toronto for the SIAM & MAA conferences. This was a blast; it's usually in a fun city, and you have lots of free time. Also, you get to see what a math conference is like and possibly interact with professional mathematicians
The housing (at least our year) was quite good; we lived in two cabins by the river/channal, which gave a nice environment. These places were sold, so the housing in 1999 and beyond may be different.
There's almost always someone from Harvard at the REU (one year there was no-one, one year there were two), and Anant is very good about having a diverse group of students.
Anant likes to have an eclectic group of people, so some of the people will be a little weird and zany/crazy. Sometimes this is good and fun, sometimes not. My year at least, it meant that most people didn't have much in common, and thus there wasn't much group spirit/joint activities. Other years I've been told that it was more successful. Also, people come from wildly different math backgrounds. Some people have played with functional analysis and homological algebra, others don't know what a group is; some have studied probability, others haven't, etc.
Michigan Tech is in Houghton/Hancock, a small (pair of) town(s). If you're into small towns in the Midwest, it's great. If you're not, it gets old real fast. And you're not near anywhere else. Some years people have driven to Milwakee or Chicago for a weekend.
We worked at Michigan Tech 9-5 (well, more like 10-4, with an hour break for lunch) on our problems, alternating meetings with Anant and working on them by ourselves. We had an office with desks (and the requisite chalk-boards), a computer lab next door, and another room for brain-storming and meeting with Anant. We cooked our own food, in our kitchens. Cars are good; there ain't no public transit. There's a Michigan Tech summer softball tournament, which was quite fun.
I don't think REUs give a taste of what graduate school is like, and I don't think that's what you should try to get out of them. In order to get any research done, one can't spend much time introducing new objects and developing a general theory; there are no REUs in ergodic theory, for instance. Instead, I think REUs are a great way to get some taste of what research can be like, as opposed to the constant stream of problem sets. There's a feeling of ownership of your topic. Also, you can learn something about an area of math that you know little about.
Within a few weeks of receiving all applications, REUs will contact you to inform you if you've been accepted, and whether you'd like to attend. Once you decide where to go, make sure to inform other programs that you withdraw your application.
If you have any questions, feel free to contact me:
nbarth@fas.harvard.edu http://www.fas.harvard.edu/~nbarth/