I'm a local to Manchester and a good mate is from Liverpool.
For Manny, it's crusty as shit but there's a lot of good spots, i'd be wary for police and seccies (security) because there's a bylaw that basically prohibits skating in some parts of the city- however you don't have to give your name.
For banks, really the only one I can think of is the BBC Banks and a couple banks near one of the Salford University building. The BBC Banks are pretty popular.
There's a fuckton of ledges around Manchester- there's some good blocks in Spinningfields that are usually waxed, one of the Salford Uni campuses has a shitton of ledges to skate that are pretty fun, and if it's on a weekend security won't bother you since there's pretty much nobody there.
There's a concrete block outside NOTE skate shop in the Northern Quarter that's ace, it's all painted up and shit. There's usually a ton of skaters outside and around NOTE and everyone's usually pretty friendly. Occasionally the staff bring out like a block to do ledge shit on and a flatbar- if you're there in summer, guaranteed the staff will be having a session outside. There's also a curb that's a pretty nice height for low impact ledge shit and slappies near NOTE. The only thing I'd really be concerned about are pedestrians. The Northern Quarter tends to have "characters" and there's an old lady who has a weird thing against skaters, she's got like a shaved head and shit. Honestly as long as you pick up your trash and clean up she won't bother you.
It's a slight trek from the city centre but there's some really cool public use spots at the Velodrome- a fullpipe and a couple manny pads. It might still be there. There's also Media City at Salford Quays, it's really sick there, however security are kind of dicks. Basically think of it like going to the MongoCorp zones in Skate 2. Just do your thing.
Parks wise- GooseSide DIY is great but currently the city is trying to dismantle it to build more office buildings. If it's still a thing in July and August, hit it up, the vibes are great round there. The two parks in the city are Graystone Action Sports and Projekts MCR. Graystone is in Salford and it's nearby Salford Uni. It's an indoor and the prices range from like £8 to £10 for 3 hours depending on the time. The staff are really sound and nice. Projekts is mixed, it's £10 for 2 hours and the vibes can be a bit weird. The guy who owns it is a born again evangelical and kind of a huge kook. The staff are alright though. You can get free entry if you're sponsored by a company- or just with people who are sponsored. Managed to get in for free because I got a taxi there with some Jart/HopKing guys. Both usually have a mix of local sponsored kiddies and skatepark heroes. Usually sponsored by Welcome or HopKing for some reason.
Shops wise, there's really only two and they're both about a five minute walk from one another- NOTE and Black Sheep. Both are good and the staff are sound as fuck, NOTE staff are usually down to chat. You can ask them for some other good spots around town, they're pretty tapped into the scene.
Lotta good veggie/vegan places around the Northern Quarter and usually all resteraunts bar shit like Wetherspoons have good veggie/vegan options so you're really not going to starve. I'd personally reccomend Rudy's Pizza (two locations, one in Ancoats and the other Peter Street? Prices are pretty okay.) that shit is great.
Venues and bars wise, Night and Day cafe is great and The Garratt is like the best shit pub and it's very cheap. Might be ketted up/drunk Uni and Sixth Form students in there but they're alright.
I'm gonna ask my mate for some good spots in Liverpool later and reply to this thread again. He's not cursed with the knowledge of what SLAP even is. Still though, enjoy your time in both. Don't mind the pungent aromas of piss and dirt-grade bud in both cities.