Hi i live near cleethorpes and no there's not much to do, if it's a nice day there is the beach and the light steam railway takes about half hour to go along track and back but you can get off and go for a walk then get back on it, my 3yr old ds loves it.
Then theres play towers, the 'slots' think ds will be too young for plesure island (more geared to 5 yrs up) and loads of fish and chips shops.
Near by there is Louth (about 20 mins away) a market town but theres a pubilc green land (Hubberds Hills) which is quite peacefull and loads of room to run around.
I would recomend Licion(around an hour away) but theres the catherdral, (sp?) castle, linconshire life musume, boat rides and shopping center, BUT be worriened although Grimsby/Cleethorpes are quite flat there are a lot of cobbled and steep hills in Licion so you may need to move the car around abit if you dont feel up to walking up and down at 7 mths prg.
There is a torist information shop on the main drag near sea front (along were libary is) which should help and thers a great farm (Hall Farm about 30/45 mins awy) just past Caster it has animals, tractor rides (you sometimes get to feed the cows potatoes), goat walks, go carts, park, CLEAN tea room, cars and bikes for younger children, big and small trampline, bouncy castles, sand and an astro slide. When i take my ds 3 and dss 9 we all love it.
Hth