We visited the Illuminations frequents when DC's were younger, we live approx an hours drive away.
We always parked up in Cleveleys (north of Blackpool) and got a tram into Blackpool. You can go through the lights on the tram and back but we always got off before the tower and walked through the 'tableau' type displays, which are really aimed at children and then got the tram back (after having fish and chips on the prom - because that's the rule isn't it?)
I don't know Blackpool inside and out but we saw the illuminations last year (it was torrential rain - I have never been so wet in all my life. But that's another story...!) and are going in a couple of weeks' time.
I'd say that the promenade is quite long so you may want to park at one end (there's a big car park at South Beach near the brilliant Sandcastle indoor water park but it might not be near enough), walk up (buggy for DD?) and then get a tram back.
But other Blackpool-based people may be able to help better than I can. Or Haven may have some advice for you as they must be asked this a lot?
We're staying at Haven, near Blackpool on the weekend. We're planning on going into Blackpool on the saturday, but I didn't realise the lights don't come on till 7ish, and that traffic is practically at a standstill. Does anybody know if it's easy to park up somewhere for the afternoon within walking distance of everywhere? We have DS (5) and DD (3), so we thought we'd walk along the lights for a short while, weather permitting, and hoped we could see enough to head back by 8pm (they're usually in bed 730, so it would get too painful for us to stay out too late nothingtodowithwantingtogetbacktoopenwine). Does this sound do-able? Not been to Blackpool for years and DH never been, and been reading such conflicting reviews! TIA.