Oddly enough I have just spent last weekend in that area. Staying in Scunthorpe infact which was a lot better than I was expecting. In Grimbsy itself there is the fishing museum, where as well as viewing the exhibits and a nice cafe, there is a 1957 trawler which has guided tours by an ex fisherman which although may sound dull, I found it very interesting and would not like to have worked on one. Very hard life indeed.
Then, as mentioned above, go to Cleethorpes and the light railway which I did and enjoyed, again they have a nice cafe and also the smallest Pub on the platform, all at the middle station.
We also visited, and you may need a car really, the Lincoln Transport museum between Lincoln and Newark, The Lincolnshire Wolds Railway, Gainsborough Model Museum which is fantastic and the best of all, a two hour standard gauge brake van trip all around Scunthorpe Steel Works, they don't do them often, but that was the highlight of the trip.
Getting back to Grimbsy, again I had preconceptions about what it was like, but infact both there and Scunthorpe were fine.
We also did some of the Saturday only services and those going to Cleethorpes and back were very busy and noisy & rather beery on the way back.
Have fun.