DT Seattle has a bad rep, yes. Some nice areas but I'd be weary walking there alone TBH. As I said I would take a taxi or car rental to Bellevue. UW is a college district so there are many small places for grub and drinks. Never been there late night so can't comment on that, just drive through there often in the daytime.
Like most cities, there are bad areas, but most of downtown Seattle is great. Restaurants are 5 star and so are the hotels. Bellevue is where all the tech wealth has congregated. Very nice restaurants and hotels there too. The U district as a more urban environment with lots of kids running around at night from the nearby university. Restaurants and hotels in the U district are 3-4 star at best and most people are just driving through. One big positive is you can afford to do a lot more in the u district than dt seattle or bellevue.
Overall, there are a million awesome things to see in Seattle, Bellevue is where to hang out in style, and U-district is cheap food and hotels.
Thanks! Tell me how far is Bellevue from me by cab? I don't mind casual drinks in student district but I also wouldn't mind a nice drink at a trendy bar with great atmosphere. Like a good place for "after work" drinks.