Hello, some good suggestions already here. Historic ships a definite yes. If you like smaller independent/alternative shops then they are in Castle Road, Marmìon Road and Albert Road. Pie and Vinyl on Castle Road for eating pie and browsing vinyl. Head to Gunwharf for discount high end shops. Avoid Commercial Road altogether unless you want Primark and H&M. Although Natty Jacks, mentioned above is very popular.
Alongside the theatres there is also The Wedgewood Rooms for alternative bands and comedy nights. If you go to the Wedgewood Rooms have a drink at The Vaults. The Guildhall has music/comedy too. If you are in Southsea on 6th Sep you'll catch the last Sunday music session in Queens hotel garden. Couple of Karaoke venues on Albert Road. Fri nights there's a ticket only sax and DJ session at the Rooftop bar, Southsea Castle.
Kite Festival is 12/13 Sep. If that's when you are in Portsmouth def need to go to it for a short while.
So many great places to eat. Farm Kitchen is a great breakfast - Turkish/British. Fuegos Street for Tacos, Eastney Tavern is surprisingly good trad pub food. Loads of great curry options. Yet to find a good Chinese. TripAdvisor list for Southsea restaurants and coffee places doesn't lie if you use that.
If you visit Old Portsmouth head to the Still and West for a drink with a view of the ships coming in and out. The A Bar is popular food-wise with local people.
For nights out drinking head to Palmerston Road and Albert Road. Gunwharf for bars. Avoid Guildhall Walk. Alternatively, the Hole in the Wall is an award winning real ale tiny pub. Gin distillery tour worth a google to see if it suits.
Tenth hole cakes are impressive to look at but imo can taste a bit plastic, Parade Tea rooms at other end of Southsea common a similar alternative. Both are nice cafes food wise and always busy. Just the cakes can be a bit meh. Loads of independent options across Southsea.
With kids, dockyard, Southsea Castle, Canoe Lake, the natural history (small) museum, Portsmouth museum, wander round old portsmouth, the fair, there's a few crazy golf options - indoor one above the arcades prob currently most popular. Splashpools and fountains may still be on. Randomly a visit to Landport adventure playground for a couple of hours...
Have a great time!