Born and raised in San Diego. Can't recommend it enough based on your criteria, but cost of living and traffic will always be an issue. If you want to be within 20 minutes of the beach, 350k won't buy you anything in some places (Carlsbad), and won't buy you much in others. Living closer to the 15 might be a better bet. San Marcos and Vista are both good options. Escondido if you don't mind being further inland (downtown Escondido is kind of a cesspool now, but the outskirts have tons of nice communities). Poway is nice but again cost will be an issue. I'm not super familiar with the towns closer to downtown SD, but I work near Mira Mesa and there are a lot of nice looking suburbs mixed in with the less nice ones. Currently I'm living in Oceanside. Oceanside is weird, because there are very nice areas (Rancho del Oro) mixed in with some ghetto areas (Oceanside Blvd offshoots), but if you live in one of the upscale neighborhoods you can almost trick yourself into thinking it's Carlsbad.
I also lived for 4-5 years in Lexington, KY. As someone else mentioned, this city is amazing. Besides the unpredictable weather, it hits a lot of key points on your list (I can't overstate how awesome the gorge is for hiking and just sightseeing), and being surrounded by rolling grassy hills gives the city a unique feel. Additionally, it's about 1/3 the cost of living compared to San Diego. My wife and I would love there again in a heartbeat if our industry had a presence there and we weren't so attached to the beach. You really can't go wrong with either city. But Lexington can certainly get ice storms and snow and torrential rain, and you're going to deal with freezing temperatures in winter and relatively hot, humid summers. In SD I lose track of the season sometimes because 90% of days are warm and sunny.
I'm traveling to Lexington for a wedding soon and writing this has me all pumped up now. It's a great place to call home. Just figure out how much value you place on the beach and the temperate climate, because those are probably the best selling points for southern California. If you can live without those things, it's probably not worth it.