Cany anyone suggest a nice, safe place to stay in Jacksonville Beach or Atlanta Beach Florida? Would like oceanfront accomodation or across the street access.

One Ocean is by far the nicest place to stay.

Check out Amelia Island - a lot safer reputation than Jacksonville beaches and you have choices ranging from 3-star mid-range hotels to 5-star resorts or even B & B's. In the mid-range hotels there's a Comfort Suites 1 block from the beach. Also there's Amelia Hotel at the Beach (right across from the beach), a Days Inn (1/2 block from beach), and a Hampton Inn about 1 block from the beach. The great thing is that there's a lot to do on the island and parking is free almost everywhere. If you want a resort, there's the Amelia Island Plantation or the Ritz Carlton.
Amelia Island has nice CLEAN beaches, minimal crime, small town feel, but all still very close and convenient to Jacksonville. Plus the area has a lot of great local restaurants that serve lots of fresh seafood! yum!

This same topic was discussed just a few months ago & Amelia Island also was the best option after all was considered. See if I can find it.

To more specifically answer to your request, check out The Inn at Ponte Vedra & the Sawgrass Marriott. I would not recommend "Jacksonville Beach" specifically, however, One Ocean REsort is relatively new & looks nice--think its address is actually ATlantic Beach which is a cute little beach town area.