San Diego: I would recommend staying in or as near to the Gaslamp District as you can - it's close to the stadium, where all the restaurants and touristy stuff and away from the airport. You can take a fairly cheap ferry across to Coronado Island for more restaurants and shops and sandy beaches too. I also went to SeaWorld. Details of my stay there in 2010 are on my 2010 Holiday blog
Houston: lots of stuff is underground. Nice stadium. I stayed a few blocks away and got quite hot walking there, but soon cooled off in the airconned stadium. The Space Center is nearby (I didn't have time to get there though, but it's meant to be good)
Dallas: never been there, but I'm considering it for September time too!
Other cities that might fit the bill could include Denver? There are nice Botanic Gardens there, and the mountains are nearby. Rockies tickets re reasonably priced. I often stop here en route to the West coast to break the journey. Might be tricky getting a Broncos ticket assuming Peyton Manning is good to go ...
Unfortunately, travel to and around the USA is pricier than it has been for some time. £3K sounds about right for a decent hotel and the cities you've chosen have reasonable prices for baseball tickets too.