I think it really comes down to what you mean by "walkable". Like, does that include a wide selection of shops and food that are walkable from USH? Not so much, but the nearby (5-10 minute drive, a very easy Uber) North Hollywood Arts District (Called NoHo) is very walkable with a lot of great places to eat, and an Amazon Fresh if you need general food (although not a lot of other shopping options--it's more food and bars). Another area would be Ventura Blvd, between Coldwater Canyon and Laurel Canyon (about 10-15 car ride, but in a different direction), and is full of great food and shopping options.
For airports, it's a trade off. LAX is much further away, but is usually easier much cheaper, and has more flight options. It's far enough away that I wouldn't really Uber, I'd just rent a car. BUR is much closer and simpler, but typically flights are much more expensive, and much more restrictive in terms of the number of flight available--it's a much smaller airport. But an Uber from there is much more feasible. I'd try there first, sometimes you get lucky, but definitely comparison shop.
As others have mentioned, it really depends if you plan on doing other things. LA can be quite spread out, and while out pubilc transport is improving, there's still not a lot of infrastructure here in such a vast city. Personally, I'd get a car.
In terms of hotels, while I haven't stayed there myself, I've heard good things about The Garland (which was founded by the actress Beverly Garland). It has a shuttle to USH (and also stops by a Metro Station, if you wanted to take that for other LA locations!) that leaves every hour. It's restaurant, The Front Yard, is surprisingly nice and sometimes a locals hang out. And there's a nearby shopping plaza with a Ralphs, Starbucks, and Rite Aid about 2 blocks away.