I have been shown an apartment that looked nothing like the place I moved in to, so I understand your concern. That said, it's completely possible to tour your St. Pete apartment before signing the final lease contract. A reputable company will be willing to let you look at your unit before you sign the lease. You may have to wait until the day of your move in if there are tenants living there up until that point, but if you politely explain that you just want to be sure that it's what you are expecting, they shouldn't have a problem letting you take a look.
When you first tour a complex, you probably won't get to see the actual unit you may move into, but after you are pretty sure of where you want to live, you can ask to be shown the specific unit you will be moving in to.
As you walk through a potential new St. Pete apartment, here are a few things to look for that you may not think of. First, check the water pressure in the showers. If it's not great, you may be able to get a new showerhead installed before you move in. Look for evidence of bugs and rodents. If there are roaches, you may see little brown specs along walls or in cabinets. Don't be afraid to really inspect the unit – bring a flashlight along. Better to find out now than later!
Check how well the doors and windows of your St. Pete apartment are insulated – put your hand along where the doors and windows meet the wall and see if you can feel any outside air coming in. Be sure the windows open properly and have clean screens. Lock the lock and deadbolt to see how study they feel. Check walls and floors for cracks or discoloring, which may mean problems in the structure or water leaks, and possibly even mold.
Check your sockets. I bring my phone charger and plug in my phone in each individual socket. Setting up your lamps and clocks and everything else is not very productive when half your electrical sockets are unusable.
Outside, check out the lighting to and from your parking space. Make sure the area is well-lit. Think about how well prepared the pathway is for rain. Look at your balcony or yard area, if you have one. If you are interested in meeting your neighbors, this would be a good opportunity to knock and say hi. Meeting your neighbors also gives you a chance to ask them what they think of living there. Are they chomping at the bit to move out as soon as their lease is over? Or have they lived there for a few years and plan to stay a while?
Hopefully, these tips will help you to be sure your St. Pete apartment is perfect for you and your needs at this time. Being able to inspect your specific unit will give you so much peace of mind, and it is definitely not an unreasonable request.