Is this the place you were looking into?
http://www.beach-house.com/hermosa-beach-hotels.html
If it is, it seems like it would be a great place to stay. I live in the area and used to running right past it regularly.
You literally walk across a bike path and you are on the sand. The beach is nice and wide, and a perfect place to play for DD. There are waves to go surfing/ boogieboarding/ bodysurfing. If you wanted to rent bikes, the bike path is great- and stretches north and south for several miles. There are a bunch of restaurants and shops within a walk of a couple minutes- in fact there is a great breakfast place next door to the hotel.
If you're into the Hollywood thing, Jay Leno performs pretty much every Sunday night at the Comedy and Magic Club, which is also within walking distance. He tests his TV show material for the week there.
I've never been inside, but from the outside, it looks relatively new and very clean. June would be a great time to stay there too.
