Southernmost on the beach is a very nice property. You won't be disappointed. If you want to save a little money, the Best Western Hibiscus is a block from there and a lot more reasonable. Either way, you will not have a problem with your lodgings.
Although Key West isn't really a beach destination as all of our beaches are man made (its a coral island), we do have beaches. In addition to the beach, as was previously stated, visit the Hemingway House and see the six toed cats. Also, the butterfly conservatory is a great place to visit and is one of my favorites. I recommend a train or trolley tour for a quick tour and history of the island. Finally, no trip to Key West would be complete without a trip out on the water. The kids would probably enjoy a glass bottom boat trip. Sunset at Mallory Square is like no other place on earth. The sunset is beautiful and the artists and performers on the pier are memorable. A lot to do in one day. Maybe you could stay two or three. You won't regret it. I love Key West.
Btw, it's KEY Lime pie, not just simple lime pie. Key limes are different than regular limes. They are smaller and much more tart. Many outside of the Keys don't use Key limes when making their fake "Key Lime Pie". Down here, it's authentic. There are two main shops to get the pie; Kermit's and the Blond Giraffe. Which is better is a matter of personal choice. Personally, I like Kermit's. Feel free to email me with any other questions. Have fun!
Yahoo Maps gives the driving distance as 395 miles (about 640 km), with an estimated driving time of about 7 hours. Be sure to visit the Ernest Hemingway house.