Hi Julian, and welcome to this board.
First of all - Atlantic Beach (East) and Ponte Vedra Beach are both great locations. AB is one of the most charming neighborhoods I can imagine. Walk to beach is easy, but walk to shopping may be a bit difficult unless you live in its southern most area with the shops around the Town Center.
The only smaller rentals that I can think of are the Seaplace condominiums. They are old (built by famous Jacksonville architect William Morgan in the 60s) but well maintained as it seems and very close to the beach (second row behind the oceanfront condos The Cloisters). Some rent for about $1,000 a month, maybe less when longterm.
As for Ponte Vedra Beach - there are condos in your price range too. Problem in PVB is: apart from the Summer House subdivision (shuttle to the beach and rather easy walk to the Sawgrass Shopping Village) and The Colony (at Corona Rd and A1A, no easy walk to shopping as far as I recall), the condos in your price range are west of A1A. When you want a relatively easy walk to the beach, you have to choose one that is close to Solana or Corona as these roads are the only ones that connect A1A with the Boulevard.
The newer condo developments near Micklers Landing (public beach access) or the older ones closer to the beach are either too large or too expensive - mostly both.
If you want to search the web, look for zip codes 32233 (Atlantic Beach, but look east of Seminole/ Selva Marina Drive only) and 32082 for Ponte Vedra Beach (east of the Intracoastal). You should also make an extended visit and consult a realtor of one of the major Real Estate companies there. Some serve the area since the 1930s. Stockton, for instance, has a very large rental inventory.
As for your other questions.
1. I think your age fits perfectly.
2. Don't know as we are not yet living there.
3. DH plays as well, there are a lot of public courses to choose from. He always books via
Golf Courses & Tee Times - Online Golf Community & Social Networking - Earn Golf Rewards - LastMinuteGolfer.com.
4. Sorry, no idea.
Nevertheless, hope this helps.
Connie