We went on the Rum Point beach through Disney last month, and had a wonderful, relaxing time. It is a small, mostly shaded beach - just about everybody there was from the Disney boat and a few people from the little Hyatt timeshare community there (I think they might own the Rum Point beach - when we bought drinks, etc. they rang up as the Hyatt on my credit card). We had beach chairs right next to the water, had some pina coladas, veggie burgers at the restaurant, a very nice time. It is not a big beach, but didn't seem crowded. Took a little while to get there, but not bad. There were small pretty fish in the water and also crabs. The Rum Point Beach Adventure (as of a month ago) also includes a coupon for free lunch from the outdoor restaurant - menu item and non-alcohol beverage per person - we're vegetarians so we took the veggie burgers and they were tasty. I didn't look really at the meat options - I think there were burgers and hot dogs and fish sandwiches, etc.
There was a great little bar too - tropical drinks! Be warned though - everything is a little pricey, especially when you take into account that the prices given are in the Cayman dollars which are worth around $1.20 of ours - so everything is more expensive than you first might think! I think a regular 14 oz frozen tropical drink ended up being around $10 US.
Lots of lizards (including the cute Curly Tailed Cayman Lizard) - very laid back atmosphere - clear pretty water - a great excursion, I would go back. Seemed very clean and safe. I haven't been to 7-Mile or any other Cayman beaches, so I have nothing to compare it to, but we enjoyed ourselves a lot.