London to Southampton

I would go with Windsor Castle. There is a lot to explore at the castle. Stonehenge is in the middle of nowhere.

Winchester is directly on the way from London to Southampton, but ... Stonehenge is a wonderful & unique experience for kids, if you ask me. It has an excellent visitor centre with indoor & outdoor exhibits, some interactive and some with live costumed interpreters at least some of the time. Also a good cafeteria. If you didn't have time to take the brief shuttle ride to actually walk around the stones (they are roped off in any case), you could still have a fun & enjoyable time in the visitor centre.

If you take the A303 from Basingstoke, it's a reasonably fast drive to Stonehenge unless you're going during peak tourist season when the hwy does get jammed up. Leaving Stonehenge, go south to (and through) Salisbury and pick up the A36. There are several roundabouts, but Salisbury has pretty good signage to encourage through traffic to stay off the local streets. The A36 will take you to the M27 and right into Southampton.

I quite enjoyed the HMS Victory and the Mary Rose ship museums in Portsmouth last year. They really made the seafaring life come alive.

Winchester might be boring for two American kids of 11 and 14, as would Stonehenge. I like Laura's idea of Portsmouth. They'd surely find that interesting, and it is a short distance from Southampton, Otherwise, consider Windsor.

Thinking back to when I was 11 and 14....Windsor. And there are some little shops in a pedestrian mall area and cafes/restaurants across the street in case they need a history break. It's a neat little town to explore.

I love Winchester, particularly Arthur's Round Table however I would also recommend Portsmouth (slightly biased!).

The Historic Dockyard is a fantastic place and being able to wander on board HMS Victory, HMS Warrior and visit the new Mary Rose museum would be very enjoyable for your children. The train from London stops at the dockyard and the entrance is a few minutes walk. From the dockyard you can visit Gunwharf Quays (https://gunwharf-quays.com) which is similar to the large outlet malls in the US where there are many shops and restaurants and is only a five minute walk away.

You can then take the train from the harbour to Southampton. This can all be done in a day and would be the perfect use of your time, stress free and very little travel to worry about, one train from London and one train to Southampton.

As someone who isn't a huge fan of boats/naval dockyards, we quite enjoyed our visit to the Portsmouth Historic Dockyards. My sister lives in Portsmouth, so we'd been there 5 times before finally biting the bullet. It was actually great fun - I especially liked the Mary Rose - which has since been un-walled (?) since we went in 2015. Fascinating.

You can buy tickets in advance online and may find some savings (we finally went because the weekend we were there, the tickets were buy one get one half price or something like that). Also included a one hour harbour boat ride.

Something else we did while visiting Portsmouth was take a train to Arundel Castle - if you think your girls might be more interested in castles as opposed to ships. I'm sure you can get a train there from London (we pass it on the way to Portsmouth), just not sure about luggage storage...

If you wanted to do Stonehenge, you could go to Bath (again, not sure about luggage storage) and pick up a tour from there - we used Scarper Tours - about a 3 hr trip - this was before things changed around at Stonehenge (I think there's a new parking lot and they shuttle you over....?) I see it's a 4 hr trip now, as they give you 2 hrs at the site - when we went in 2012, there wasn't much of a visitor centre. They have 2 tours a day - one at 2pm. https://www.scarpertours.com/