Beacon Hill is great. I've lived a little ways away (in Columbia City) for almost ten years and I know a lot of folks who live on Beacon.
The RE market is perhaps being hit harder in the south end than the north, more foreclosures, because (a) more lower-income people losing what they had owned and perhaps too zealously refinanced, and (b) I'll bet a lot of weird half-assed real estate "investment" happened down here during the fast and furious RE years, because houses were generally lower priced, and is now falling apart. So, I'm not surprised you could find good deals down here.
So why is/was it lower priced in the first place? There's some weird thing in Seattle culture that is very north-centric. It's like the city forgets that anything exists between I-90 and SeaTac. I moved here in 1992 to go to grad school and never really considered this until friends of mine moved to Hillman City from Wallingford in 1997 or so. Wow! Who knew this was all there?
I think part of it is about race. The Rainier Valley was one of the few places (with the CD) where blacks lived. Beacon had and still has a high concentration of Asians. There are plenty of white people down here too, make no mistake, but I think the major media outlets (both mainstream and high-profile alternative) are pretty north-end focused, and the Asian and black communities have their own media...anyway, I think that's part of what has historically kept the south end "off the radar", and still does to some extent.
Anyhow: There are lots of nice places along Beacon, from the north end near Amazon and all along the ridge. Close to downtown, several walkable urban districts, good parks and green spaces. Beacon does have more airplane noise than other neighborhoods but my friend who live there say it is not bad. I love where I am but I could easily see enjoying life on the Beacon ridge.
The south end in general has a bad reputation for crime, but in truth, if you look at the police stats by neighborhood, it is not any worse than other parts of the city. Certainly not Beacon Hill per se. Downtown, the U district, and Fremont have crime stats as bad or worse--go look at the police web page and see for yourself. Every part of the city has sketchy areas and you'll know them when you see them (like the intersection of Rainier and Henderson).
The elementary schools closer to the north end (Kimball, Beacon, Maple) have better reputations than the ones farther south (Dearborn Park). Lots of families from Beacon send their kids to Orca in Columbia City too, if you're into the alternative school mode.
The middle and high schools in the south end don't have a great reputation, but I have a feeling that the demographic shift from the last ten years of gentrification in the south end are going to play out and make some changes in the upper grades as they have in the elementaries. If you don't have kids yet you have a long while to worry about this, though.
A great way to get your fingers on the pulse of a neighborhood is to of course visit/hang out there, and to find local blogs. Bear in mind that as with topic-focused blogs, neighborhood blogs tend to be run by busybodies and dwell more on what needs improving than on what's going well. (Present company included, of course.)
Hope this is helpful! Good luck with your house search, whenever it comes along.