London Hotels? I have narrowed it to these..

I would like something that is central for all the sightseeing in London.
We are 2 adults and 2 kids. (17, 13).
Something close to the tubes and convenient.

Also the Park Plaza I was talking about is Westminister not the County Hall one.

Of these three, I have stayed at the Premier Inn County Hall, maybe three times. It certainly is centrally located, and while it is well located for tube, bus, or taxi, note that it is a good place to be for walking around. Tired in the evening? Stroll along the South Bank. Visit little restaurants that (as I recall) seem to be family friendly. Visit Shakespeare's Globe, Borough Market. Cross the river and visit the Tower.
Lots of bridges. You are also right by Waterloo Station with bank machines and a supermarket and trains to places you may want to visit.

Premier Inn does have something about family-friendly rooms on its website, and it seems 4 might be accommodated. But you would have to check it out.

Note that Westminster Bridge is always mobbed. However, there is a little no traffic zone (or was) right at the Premier Inn's entrance. Kind of nice to be able to step away from the crowds.

thank you!

Have you looked into the London School of Economics which rents out rooms as well.
lsevacations.co.uk. This is when classes are out.

Thanks! Just did and all booked.