Well, the pair programmers would be mentors in #3, but the fact that #2 realizes they need to assign a mentor says a lot of good things about them.

If you're really going to limit this experience to one year, as noted by others #2 or #3 are your best bet, and it sure sounds like #2 is a better/surer fit.

What matters most is what that one year on your resume is going to look like (e.g. how will you be able to boast of success) and what you'll learn about working in the real world. #2 sounds by far the best for those two goals (e.g. pair programming is not widely used). Also note that is sounds like #1 and #2 are going to be a lot more committed to making the relationship work, whereas one bad senior pair programmer at #3 could be the end of your experience there.

Good luck!