Hi Mate.
Im a Sandgrownian (as they call us Blackpool folks!!!) You can park across from the Pleasure Beach but its very busy with traffic. I see a lot of motorhomes parked at the opposite end of town near Cleveleys (its packed at the moment because of the ferry stuck on the beach!!!)
There are a lot of caravan parks in and around Blackpool but to be totally honest with you I wouldnt even think about wildcamping anywhere near the Promenade unless you want to spend the night looking out of your window for the next idiot banging on the side of your van as they stagger past.
The nearest site I can think of with hookups etc and open this time of year is just off the Yeadon Way next to the Yeadon Way Pub and petrol station. I think you access it from Lytham Road, its at the back of a working mens club but is always busy and open all year. Its also only a stones throw from the Promenade and the Pleasure Beach. Ill try and find you a phone number next time I pass it and post it on here.
If your interested in the Pleasure Beach Id wait till March when they do their "March Madness" offer of a wristband for £15.00 (at least thats what it was last year!!

) and the Tower is open then as well at weekends.
Dont forget the latest tourist attraction laying on the beach at a nice 60 degree list, should be there for at least another month before they manage to get it floating again....Lived here all my life and never seen anything like it before!!
Oh and dont forget we are only an hour away from the Lake District (I should get a job with the tourist board!!!

)