If you have an energetic dog, I can recommend the West Wight loop of Freshwater Bay, Tennyson Down up to the Needles Old and New Batteries (National Trust) plus the rocket site, round to the remains of Hatherwood Battery and Headon Warren (lots of rabbits and the odd viper), into Totland Bay and then back through Freshwater. It's 10 or so miles. Pub opportunities depend on route. The Highdown Inn is off the back of the down; there's the Waterfront Bar in Totland Bay, The Vine in central Freshwater opposite the chip shop, and the Red Lion near All Saint's Church, where if you have a mind to you can trace bits of my family line back to 1750-ish.
The Red Lion (not child-friendly) is a good starting or finishing point for the circuit of the Yar estuary along the old railway line into Yarmouth where there are more pubs (The Wheatsheaf, The King's Head and The Bugle – there is also The George, but that is too expensive for mere mortals) plus restaurants and Yarmouth Castle. The castle (English Heritage) will take you all of 10 minutes to look over.
Carisbrooke Castle (English Heritage) has some good walks around it even if you don't go in. If you're a long-standing member of Historic Scotland, of course, you'll get reciprocal free entry to English Heritage sites. Non-military, but interesting is Osborne House (English Heritage), though bits of it have served as a naval training academy and there's the royal children's play fort and trench system at the Swiss Cottage.
Depending on when you visit the IW Steam Railway at Havenstreet may be having one of its history weekends. The 1940s weekend (1-2 July) sees loads of WWII vehicles on display. There's a Victorian weekend too (5-6 August), mainly populated by overheating re-enactors in period costume or uniforms.
The wargaming club on the island is no more, and has fragmented into loads of small groups. I'm sure something could be sorted out.
Visitors are welcome at Fighting 15s by arrangement. I can make coffee, and while you are admiring how the spoon stays upright in the middle of the cup, you can also look out of the window and across the Solent at Hurst Castle.
Ian
Fighting 15s