Frank, I know from travel experience you are in one of THE deepest no-radio holes on Earth! With no elevation you are in some trouble with a handheld. I run a KG-UV1D and with the rubber ducky down there it gets mighty quiet! If you're going to try to hit Clearwater or St. Pete, even if you're five stories up, it ain't gonna happen. 2m and even 70cm are basically "line of sight". That sea level stuff is a bear to overcome without antenna elevation.
One repeater you may want to try is the Redington Shores system that has several towers and I've hit one easily from there. Their website is:
WD4SCD Repeater Page
Try 147.030 in and 147.630 out with the NORTH tower PL of 103.5.
That should be about 4 or 5 miles for you and you should be able to hit it. The advantage here is that once you get in to any of the repeaters on that net it sends you out on all of them. Somehow they have an elevation of a couple hundred feet (must be a commercial tower they use?) and the system works.
Other PLs for those same frequencies - and try them all - are 82.5 and 192.8.
Also, I've found as have most users that the 70 cm band (440-450 mhz) gives good results over low terrain even with obstructions from buildings and low hills. I live in the hilly Ohio Valley and have a 70 cm repeater 28 miles away, as the electrons fly, that I can hit anytime with the rubber ducky antenna. I cannot touch their 2M repeater with the H/T even hooked up to a base antenna. These Wouxuns only give you 2 watts on 70 cm but they do seem to work under some conditions.
Try the Pinellas Park 70 cm repeater (maybe 5 miles?) at
442.625 in and 447.625 out. They do not use a PL tone. I've used that one when I was passing through and even hit it from the car without using the mobile antenna.
There is a repeater in Largo with a net meeting Wed. nights at 8pm and tuning in there may let you hear and see if you can get there. 146.970/146.370 with a PL tone of 146.2.
Go to the repeater database search I use and see what you can drag up, trying to use some of those 440 frequencies:
Amateur Radio Repeater database - Updated daily
Good luck with it. There is a way and there will be a frequency or two.