Where will you be coming from? The drive from Miami down to Key West takes nearly 4 hours, so that's a pretty long drive for one night. Any chance you could stay two nights?

Since the keys are coral, natural beaches are practically non-existent. Rather, the vast majority of beaches are man-made and small. There are 4 hotels in Key West that're on the bay side that might fit your bill (excluding the good beach). The Pier House has a small beach, the Ocean Key Resort is a great hotel, but with no beach, the Hyatt (on Front Street, there are 4 in Key West) has a postage-sized beach, and the Westin, which in my opinion wouldn't fall into the "romantic" category, and which also has no beach.

The Sunset Key Cottages are an 8 minute ferry ride from Key West and are apparently lovely. I haven't checked the prices recently, so have no idea how expensive they are these days, but they're run by the Westin in Key West. On the bay side, those really are your only options.

rates usually drop in the Summer due to the heat and humidity so you can buy more luxury... Islamorada is half way to Key West and can be a great and faster alternative... there are also choices in all price ranges... have fun

I haven't stayed there, but Luxury Link is always showing specials for the Cheeca Lodge in Islamorada, which looks pretty nice:

www.luxurylink.com/fivestar/hotels/islamorada-florida/cheeca-lodge-and-spa

I haven't stayed at Cheeca Lodge in decades, but it had a great reputation then, and still does. If memory serves me, though, I think it may be on the Atlantic side. Another place that I'd forgotten about is the Moorings, which is just next door, and it also has great reputation.

http://mooringsvillage.com/moorings_village_tour.cfm

We stayed at the Cheeca Lodge at Islamorada about 15 years ago - and loved it. Went deep sea fishing the next day and then beat it back to Miami for our flight home (we had earlier been on a short cruise out of Miami) - and that was just fine as the Xmas Holidays were kicking in on Dec 18th or whatever it was - and the room prices were tripling.

Assuming it still lives up to the good rep - go for it.

You can walk out the dock and enjoy seeing fish in the water.

And yes, it is on the Atlantic side.