You might try the pool at Tay Ho Hotel (link below). My son takes swimming lessons there.
There are two pools and it hasn't been very crowded on weekends. There is a mix of VN and expats that use it.
The admission fee for an adult is 30,000 VND. The pool is clean enough, though the grounds are not as clean as a Western-style hotel.
It is easy to find -- look for the hotel's huge billboard on Xuan Dieu, turn there and follow the road to the end.
http://newhanoian.xemzi.com/en/venue/show/1973/Tay-Ho-Hotel
I tried monteromano's suggestion today (thanks!)-
-it's a 25m pool (not very wide) on the east bank of west lake.
-At midday it was virtually empty.
-It costs 30,000 (same as the much bigger Sao Mai).
-It opens from 5:30am to 10pm (I think!).
It's an outdoor pool and from a sign in VN that I couldn't really understand I think it's open till the end of November.