I'm not sure what a "tall ship" category includes. Google tells me a large, traditionally-rigged sailing vessel. To me, that would be more like the Cutty Sark - a clipper ship - in Greenwich. That is fun to visit when in London. Read current reviews, but a few years back, we clambered all over. Another fascinating London ship is the HMS Belfast in the Thames. Good audio explaining usage in WWII and earlier as well as Brit nautical traditions - rum allocation, etc.
Portsmouth Harbour options at the museum - Main entrance side: Victorian Warrior- climb all over and explore freely; Nelson's Victory - under renovation but accessible for walk throughs with a good audio guide, lots of canons!, story of Nelson's last victory at Trafalgar; the Tudor Mary Rose - incredible resurrection of a 1500s era vessel - exhibit is very good with lots of artifacts, views of the Mary Rose and some videos at beginning and end to help a 10 (or 60) year old process the exhibit; WWI Gallipoli HMS M.33 - video story and walkthrough at your own pace, fascinating camouflage paintwork; several museum style exhibit halls with nautical artifacts and ships. Using the ferry provided by the Dockyards to the opposite side of the harbour - fascinating Explosion museum of weaponry through the ages and submarine HMS Alliance and submarine museum. Also, harbour ferry tour available. There are British naval ships docked at Portsmouth along with French ferries coming and going, so interesting things to see.
I found the website for the Dockyards a bit confusing and overwhelming when I was planning. On the ground, it's more obvious, but I was not aware of the necessity to be tied to a ferry schedule until on sight. The walk between the submarine museum and Explosion museum (after a ferry ride from the main museum site) is about 30 minutes - so my plans to do both in one day quickly and efficiently was no good. The HMS M.33 also had shortened visitor hours that I didn't expect. Once at Portsmouth, it may be worth taking a few minutes to "map out" a personal agenda for your visits.
We stayed at the Premier Inn Portsmouth Dockyard. This was my first experience of a Premier Inn. I know it is a favorite chain with many on this board. It is less than half a block from the Dockyards entrance and walkable (maybe 3 blocks) from the train station and ferry to I of W). My hotel review - I can't really complain. Very clean, staff was very good. Breakfast was acceptable, but nothing I would return for. The beds were not particularly comfortable, but room was larger than I expected. I think I am not a PI fan, but this place did fit the bill nicely for back and forth to the museum and transport. Price was good.
Also walkable from the PI and Dockyards is a mall and restaurant area - Gunwharf Outlets. We had a couple meals there with a number of chain type options, Wagamama, etc. As non-drinkers, we weren't interested in the pubs near the PI, but they were popular. There is a restaurant at the PI, we used only for breakfast.
It is probably a 45 minute walk from the PI or Dockyards to Southsea Castle and the D Day museum. I was given bus directions - major bus station right outside the train station. As we walled to the bus station, I saw a taxi rank and grabbed one of those instead. Quick ride to that area. We strolled back along the waterfront.
I don't know your itinerary, but Portsmouth was our last stop before Heathrow and return home. We took a National Express bus from the Portsmouth bus station by the train station direct to LHR and our last hotel - the Hilton Garden Inn. Much easier than train back into central London.
Summarizing - getting around Portsmouth was a breeze if the main interest is the Dockyards and SouthSea area. Tap and go for buses, taxis if desired, walkable to IOW Wightlink ferry and train. If you wanted to try the Southsea hoverport with the grandson, this might be a taxi ride - or a longer walk.