I did the NIH summer program and I can say that it was brought up at every single interview and the interviewers were impressed with the program. I have no basis to judge whether there are other programs out there that are better, and I'm sure there are, but the NIH SIP is an excellent program.
You're not too late yet, just start contacting the professors you want to list as contacts and get it out the door asap. Also, the housing thing isn't a huge issue. At least for my institute, they sent out a list of contact info for all the interns that would be there so we could coordinate housing if we wanted to. People subletted apartments for a great deal, so don't let that deter you. You get a sizeable stipend, and that will more than cover your living expenses for the summer, so you'll even pocket some of that money.