Ah, Seattle. I miss it so. 
Especially since North Carolina in August is one unremitting sauna bath.
[url="Seattle Maps and Orientation: Seattle, Washington - WA, USA"Here is kind of rudimentary map of Seattle, which you can refer to for this post.
Belltown is right on the water, slightly north of true downtown. (On the map, it would be on the water directly below “Queen Anne”.) It’s part of downtown, and has all the associated problems: homeless people, some drug-dealing, no grass. The apartments are almost all new (Belltown is experiencing “urban renewal”, and there are lots of restaurants and clubs. If you want the true exciting urban lifestyle, Belltown is a good bet. It is not 100% safe after the bars close, and it can be noisy – basically, all the pros and cons of any “happening” city neighborhood.
Highway 99, also known as Aurora Avenue, runs north and south through Seattle (and as far south as Tacoma and as far north as Everett). At its best, it is strip malls and automobile dealerships; at its worst it is no-tell hotels and prostitution. Although there are really nice neighborhoods within 2 to 3 blocks of Aurora, I second the advice that you really don’t want to live right on it, or right next to it, if for no other reason than it’s a very busy street. On the map, 99/Aurora runs roughly just slightly to the left of “Freemont” and “Green Lake”. (It doesn’t run right through downtown, however; it bypasses it Freemont is very cool and very convenient to downtown, as Ballard is as well. Ballard is historically more working-class and Freemont more hippy, but property values have gone up so much that they are both basically new-urban-revival. Freemont clings to its hippy-ish past, but in a way I think is pretty self-conscious. Queen Anne is lovely – much more established and wealthier, more families, some good restuarants, lovely parks, but no clubs and not much nightlife. I lived on Queen Anne part of the time I was in Seattle and I really liked it a lot. Safe, pretty, leafy streets to walk my dogs, and a bus ride to downtown. You’ll see that the map says “Pacific University” – I’m not sure why, that’s not an area of town. Pacific University is actually in Oregon; this marks the location of Seattle Pacific University, which is on the north side of Queen Anne, near the Ship Canal. The north side of Queen Anne is not as desirable as the south side, which is closer to downtown, but you may find a decent apartment over there because there does tend to be some student-geared housing. Magnolia is west of Queen Anne, where Discovery Park is shown on the map. It’s a lot like Queen Anne, but further away from downtown and even quieter. Capitol Hill is the gay district – very cool, lots going on, but as you’ve discovered, a wide range in housing from absolute fleabag shitholes to multi-million dollar condos. To the extent Seattle can be said to have a “bad neighborhood,” the backside of Capitol Hill (the Lake Washington side) is edging into it.
As for sub-neighborhood: The University district (on the map, “University of Washington”) has some good values, again driven by the students. But just like all student-type housing, some of it is crap. The Woodland Park/Green Lake area is further away from downtown, but might be a good bet for a decent apartment at a decent price, and is still on the bus line. (Green Lake is a great place to go for a walk or run, BTW; it’s 3 miles once around and you can watch the crew teams practice.) Phinney Ridge is just north of Fremont and retains some of its funky feel. Ravenna is tucked between Green Lake and the U District and is very pretty but can be spendy. Madison Park is small, manicured, quiet and park-like, tucked in between the Arboretum and Lake Washington, but tends to be expensive. Alki is in West Seattle (the land directly below “Elliot Bay” on the map) and can have some good values, but commuting to downtown is a bitch.
And that’s worth mentioning: Commuting in Seattle is a bitch, period, unless you’re on a bus line. So you may want to know where you are thinking of working before you make a decision on housing. If you’re working downtown, public transportation is definitely the way to go; parking is hella-expensive (like around $250 a month, and no, that’s not a typo), so you’ll probably want to know where the nearest bus line is to your new apartment.
I hope you really enjoy Seattle; I absolutely love the city. Ride a ferry for me. 
Just saying, if you can’t find a place in Fremont, being right next to the 
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