Basic science probably is not practical on a med student schedule, unless you want to take a whole year off to do research (some schools have a "research track" where you can do this without doing a full PhD). But every department has some chart review that they've been kind of kicking around that they need some motivated med student to help out get started, and you can usually make substantial progress on this during a one month research elective. If you want to have a shot at something publishable at the end of med school, this is likely the way to go.
Agree with others that cold emails to people that you've worked with is a good way to go. This kind of clinical research probably isn't going to be advertised on a website, as they're fairly small projects.
Finally, this is true generally and something to keep in mind--unless you really have a burning passion about a specific question, the mentor you pick is probably more important than the project they offer. So if there's an attending that you've worked with and you get along well with them, I'd suggest trying any semi-reasonable project with them over something with a mentor you don't get along well with.
