From Lakeside you could take CA67/78/79 through Borrego springs to the Salton sea and head North on CA86 towards Indio. You could easily spend a couple of days enjoying Joshua tree NP. We enjoyed staying at Indian cove campground ! I can't comment on Quartzsite but it's up to you if it appeals to you or not. I would check before going though as I believe it's home in the winter to thousands of 'Snowbirds', RVer's that head south for the winter. You could also head through Amboy to Needles and Kingman and and take Route 66 through Seligman on route to Grand canyon.
(Moderator note. If this is part of an ongoing trip please post all further updates and questions in this thread to make it easier to follow where you have been and what has been said.) Thankyou