I'm starting to detect a trend here- I'd say try something new and get a Road King.
I was in a similar situation when I had a day to myself on my last business trip to San Francisco. I don't get to see many curves where I live so I was really looking forward to having a good corner carver to ride while there. I looked for a sport bike of sorts to rent and couldn't find one (mostly I wanted a Buell or a ride on the new BMW R1200GS but neither were to be found). Time was short and Eaglerider was easy to work through so I opted for an HD Road King. I''d never ridden a cruiser of any type and got excited to finally try one out.
I have to say I had a lot of fun. Made the day feel like a real vacation: cruising at a less than break neck pace, taking in the scenery, having loads of fun with the torque, and just enjoying the cruiser experience. The bike was sweet. It looked, sounded, and felt just like you'd want/expect a cruiser to.
If you do end up getting a Road King get the one w/o the beach style bars if possible (I think the Classic has normal bars and the Custom has the beach bars, someone correct me if I'm wrong). I was on it for about 6 hours straight through a lot of twisty roads. My wrists were pretty sore from the bend the bars put on them. It got to a point where I didn't want to shift but with all the torque shifting was kept to a minimum.
Second, if you have to or want to wear a helmet bring your own. The helmets at Eaglerider were fugging disgusting!!! I had my choice off a rack and they all had hair, makeup, and all kinds of leftover human head parts in them. Really gross. I went straight to Cycle Gear and bought a RF1000 (I was looking for an excuse anyway but I'd have bought something cheap regardless just to get away from that filthy disease infested piece of garbage I had).
If you are really set on a sport/sportier bike you may want to look to a local BMW dealership. There are a number around that rent bikes.