Yes, if you do all the Historic Dockyard, you definitely need at least 2 days. I enjoyed the harbour boat trip, if the weather is clear.
The beach goes basically from the Harbour entrance down to Eastney, which is miles. Water quality is generally better at Eastney. They're still doing up some of the esplanade round Southsea Pier. There's also Clarence Pier untoward the harbour end - if you walk along the front back towards the old town, they've got new information boards, which went up last year with the sea front works, tells you quite a bit about the history. There's also the Garrison church on the orherside, which you can go in sometimes, but uess you've got English Heritage or are really into church history, I probably wouldn't bother. Then as you go round, you've got the Round Tower and the Square Tower.
I like Portsmouth Museum, which is quite a traditional one. It's got quite a bit on Conan Doyle as well.
The D-Day museum with its embroidery is great.
Gunwharf Quays has lots of shopping and restaurants, mostly chain places. Spinnaker Tower is worth going up if the weather is clear, but not if it isn't.
You can walk pretty much all the way from whichever Tower is closest to the harbour entrance to Eastney. There are various naval memorials along there, on the sea side and on Southsea Common. Also the hovercraft to the IoW goes from Clarence Pier, which can be fun to watch if you've never seen it.
Walk further along, there's the D-Day museum, as mentioned, (public toilets in the car park there, too.) Also a good chippy there, can't remember it's name, Blue something. Southsea Castle is interesting if you find the history of forts interesting.
Up by Southsea Pier, there's the model village.
If you have transport, do go up on Portsdown Hill and look at the view - it's brilliant. It was really clear Saturday morning, might not be so great if the weather's bad... There's also Mick's burger van up there, which is a bit of an institution, but it can get long queues. And it's probably not do great if you're vegetarian. Fort Nelson with the Armouries museum is also up on Portsdown Hill. It does tell you about the history of the Palmerston Forts, but unless you're interested in the history of cannons and artillery, I'd probably give it a miss. If you are into that, it's great.
You need a week...