I live in St Albans and I agree with what has been said. This whole area is crowded and schools are feeling the pressure. During the last election, a candidate stumped up to my door and told me how they want to release some green belt land to build 400 affordable homes. I asked about corresponding traffic improvements and schools - their response was "I don't have any school aged children so I didn't consider that" !!!
Anyhow, one main reason for the crowds is the quality of the education. There really are no "bad" secondary schools here. There are a few that are worse than others (Nicholas Breakspear and Samuel Ryder), some that are perhaps average (Marlborough, Loreto and Townsend), some that are well above average (Beaumont, Sandringham, Verulam and STAGS (which is St Albans School for Girls, which is NOT St Albans High School)). There are two highly regarded privates (St Albans School (which is often referred to as St Albans School for Boys, although that is not its name) and the previously mentioned St Albans High School. If your children are exceptionally bright, they can try for Parmiters in Garston (Watford) or if they are in the top 0.5%, Dame Alice Owen in Potters Bar. You also aren't too far from Haberdashers Girls if you are thinking private and can't get into St Albans High School. The other North London privates are also reachable.
I don't know a lot about the Harpenden schools, but St George's has a tremendous reputation.
I am lucky enough to have a son in the St Albans School, where he has thrived. It is an outstanding place to learn, and I can't recommend it enough.
For a state education, the place to live is Marshalswick. That would put you into the catchment area for both Sandringham and Beaumont. For STAGS, you need to essentially be on the doorstep - too far away and you'll end up at Townsend (again, not a bad school, just not as good as STAGS).
Good luck!