We will be visiting Los Angeles for 4 nights and I would like to find reasonably-priced accomodation for a family with a four-year old and 1 year old. Preferably Santa MonicaVenice Beach area, but am open to other areas as well.
Catherine

It depends on your definition of "reasonably priced". Near the beach areas I don't think you'd find anything cheaper than $50/night.

Venice is to say the least sleazy after dark and not the place for visitors with 2 small children, Try the suite hotels many are suprisingly inexpensive especially in the South Bay Orange County areas.
Santa Monica is out of the way for most tourist destinations in Southern California. If central is your goal the hHollywood area beats Santa Monica by a long shot.