There are several parks I can recommend. Bay Bayou RV Resort
http://www.baybayou.com/ is in Tampa. The campsites are grass or sea shell and there are no-see-ums. If you don't know what that is, you will when you get there! It is a straight shot to the fairgrounds, but the traffic can be a bear at certain times of the day. Mileage-wise it is close and can take approx. 45 minutes to the fairground in heavy traffic.
The park we are in is Three Lakes RV Resort
http://www.sunrvresorts.com/three_lakes. Every year there are people who stay here for the show. Most I've spoken with say they prefer cement pads here as opposed to the grass sites. It's just under 50 miles ( a little under an hr to get there).
Another is now part of Sun Communities as well.
http://www.sunrvresorts.com/tampaeast/. I believe this park is only one exit down I-4 from LazyDays. Last time we were there they had all grass sites. Not sure if that has changed. This park is the closest of my recommendations to the fairgrounds, and since it isn't far from Lazydays, you can share time with the lucky ones who are staying at Lazydays! The only thing is that they charge $12 more per day for special events including the rv show. Not a big deal but just wanted to inform you.
There are lots of parks but many may be full for the season.