to be serious for a moment, here's all the crap i can think of right now. if there's anything specific you have in mind, i'm sure i can think of something that foots the bill.
museums:
pink palace museum (also has an imax and planetarium...and good food!)
fire museum (it's awesome, for real)
there's also a small police one on beale...admission is free
peabody place museum (you almost never hear about this one which is a shame because it's small but it's not crowded and has beautiful artifacts)
gibson factory (i think it's kinda overrated but it's just me)
civil rights museum
stax museum (warning: in a baaaaad area so be careful)
graceland
(also in a very bad area and overrated, overpriced, and just anticlimactic. oh and re: spaghetti warehouse, there's one in a better area downtown, you just have to look for it)
mud island (not really a museum, but it's there and there's a scale version of the mississippi river. but nothing else really unless there's a concert there which...there isn't.)
sun studios - fyi this won't take long. it's like a short fifteen minute speech and you get to look around the tiny room. that's all.
midtown is lovely. the garden district has some gorgeous homes that you can drive around and see. also in midtown is cooper/young, a sort of trendy eclectic area with little shops and restaurants. i've only eaten at two restaurants there so i'm not a huge help (memphis pizza cafe - a local chain, their pizza's not bad; celtic crossing - i got a bad impression since i went on thursday - be careful, thursdays are uh...something important in the cooper/young district. everything's packed).
barbecue is a must. you just HAVE to get barbecue while you're in memphis. pulled pork and ribs are our speciality. dry ribs are the memphis thing (no sauce, just the rub) but you won't be tarred and feathered for ordering them wet. i hate dry ribs. but i prefer pulled pork so the work's done for me. also, we put slaw on our barbecue sandwiches, fyi. i prefer corky's. rendezvous is too expensive, but it is downtown. another big place is neely's but i've never been since their locations are in really bad areas.
chicken is another big thing here. it's simple: you HAVE to go to gus's. there is no other place to try. theirs is the best. the one downtown on front street is my favourite. there's another in the 'burbs near my house but theirs is...just okay.
bars? beale street has a ton of them. for recommendations it really depends on what you want. if you want booze and bbq, try pig on beale. for cajun, try king's palace cafe. if you want familiarity, try hard rock. alfred's and dyer's have awesome burgers. if you just want to drink though, try silky o'sullivans or rum boogie. do not go to blues city cafe. gross. if you want less crowds, try the pinch district. it's still downtown, further down main street. if you don't want to drive (though you can since traffic in that part isn't too bad) just hop on the main street trolleys. tj mulligan's is my favourite, and they have locations all over town too. their roast beef is LEGENDARY.
other shit to do? not much. we have a few shopping malls if shopping is your thing. saddle creek is a collection of some upscale-ish shopping centers in germantown. there's a nice outdoor mall in collierville. wolfchase galleria is a good indoor mall. oak court mall is in memphis but it's kind of iffy these days. any other malls are in horrible areas.
if you like outdoorsy stuff, we have some parks around here. tom lee park is downtown on the river, but for huge spaces i recommend shelby farms, right on the tip of memphis before you get out to the burbs, off walnut grove. it's huuuuuuuge, and easily accessible from the interstate.
like zoney said, the peabody hotel ducks are cute. i recommend going in the morning though, the afternoon thing is kind of anticlimactic. i like watching the ducks arrive, not leave. don't plan on hanging around there for breakfast though, the restaurants are pricey. if you want to walk a few blocks or hop on the trolley, there's a blue plate cafe a few blocks down. their pancakes are great.
any other stuff though, feel free to ask and i can hopefully steer you in the right direction. and be careful driving, it's the easiest city i've been to where one minute you're in a safe area, the next, not.