StackMob or Parse if you want a (client-side) JavaScript API with user management, facebook/twitter integration, data store (with geospatial), and push notifications.
StackMob also lets you host your website.
For more flexibility, less service lock-in, and cheaper scalability: I would suggest CouchDB (though you would likely still use a hosting service like Cloudant). CouchDB can host your website, and provides a HTTP API for storing data, to which your client-side JavaScript can make REST calls.