Harrah's is my favorite one to stay at. I love the pool. It is in the marina, but when you stay at the four Harrah's properties...Harrah's, Caesar's, Bally's and Show Boat, you can ride the shuttle between all four. If you're only a Gold Card member, be sure you bring that little slip of paper they give you when you check in, otherwise you can't get on the shuttle. We always hop on the shuttle and go over to Caesar's and do the outlets. We also like to go over to the Pier Shops at Caesars, go up to the third floor and sit in the adirondack chairs, with our feet in the sand, and just look out over the beach and ocean. There's also a Rain Forest Cafe right near Caesar' on the boardwalk.
There are also jitneys (little buses) that stop near just about every hotel. The last time we rode that it cost $2.25 pp. Sometimes the free shuttles take forever to come, so we hop on a jitney instead of waiting.
The weather in early June is usually pretty nice, highs in the low 80s.