I grew up in suburban Boston. It was a very nice town - we lived on an acre of land, with woods behind the house. Drive 30 minutes in any direction, and you got basically - woods. Maybe some ponds and fields, with scattered houses and suburban town centers between. The city (a pretty nice one) was 30 minutes away. You could get to waterfront, in Boston or Salem or Nahant, but there aren't really beaches in most of Massachusetts (outside of Cape Cod). It did have a massive amount of history, though - in that 30 minute drive was basically everywhere significant to the birth of the USA.
I'm on the peninsula now, in the hills. 10 minute walk to a suburban downtown. 3 minute drive (or ~20 minute walk) and we're on some Bay trails. 5 minute drive and we're in the mountains. 5 minute drive to a massive lake over the San Andreas. 20 minute drive and we're on the beach at the Pacific Ocean. 30 minute drive (or 40 minute Caltrain) and we're up in SF. 30 minute drive and we're in downtown San Jose.
I'll grant you the Santa Cruz Mountains if you're on the southern end of the Bay. You've also got the hills in the East Bay and various options in Marin and points north if you're in Marin.
But Boston, in addition to various coastal walks has a bunch of nearby parks and small mountains/hills to the west and in southern NH. Also tons of sea kayaking/canoeing. Depending upon where you live, bigger peaks in NH are maybe 2-3 hours.The Sierras are further than that from the SFBA.
Don't get me wrong. The Bay Area has great recreational options but so do a lot of other cities depending upon what you're looking for.