You could go to Popworld which is just up a little lane from Revolution, I think it opens at 4pm on Saturdays. Lots of cheesy music and cheap drinks. It's on the Bigg Market which is a square of pubs, some restaurants and takeaways and can get a bit rough and/or rowdy later on at night but honestly there isn't usually a whole lot of trouble or if there is it's usually between drunken groups falling out with each other etc. There is security on the bars and often police presence to deal with anything that does happen (I appreciate I'm making it sound scary, it isn't my usual choice of night out but I would go there without any fear as a normal person not trying to start fights or aggravate anything - appreciate you can always be unlucky 🙃).
Opposite Popworld on The Bigg Market (cross the little road) there are various other bars playing cheesy and/or pop music. There's also The Old George which has music, often DJs in the outside courtyard bit, it gets very packed as it's quite narrow inside but you can spill outside for more space. All of this area of town has loads of pubs and bars so you can wander and see what you fancy. There will be so many places I don't even know about as I don't get out much these days.
If you'd rather avoid that area there is Sgt Peppers up the top end of Newcastle CC near Haymarket metro. All of the city centre is walkable. I used to go years ago for cheesy music and haven't been for a while as I'm old 😅 but it was always good.
The Pink Triangle as suggested is the 'gay bar' area which is good fun, it's just on the other side of Central Station from Revolution. Gossip, The Dog, The Dog and Parrot are bars there with music and dancing (well the first 2 definitely dancing). Around Central Station itself there are various bars I can't remember the names of including some down steps into cellar type places or one up little steps just left of the station now called Tickets I believe, I used to love that when it was North bar and then Xerox but haven't been in the latest incarnation. They always used to have good music but maybe not cheese or pop.
There are also some places with Latin music like #1 Grey Street (address number 1 Grey Street unsurprisingly) and Revolucion de Cuba. 1 Grey Street goes on LATE. My husband often goes there as he's Mexican and he and his Spanish-speaking friends like it, it's not really my cup of tea (I have two left feet ðŸ¤) but definitely atmosphere, dancing and people who want to have a good time without hassle.
To add to my very out of date knowledge, I will say: when you're out you will very likely find people to chat to (or who will chat to you) and you can ask where they're off to or what and where they'd recommend for dancing or certain music. People are generally extremely friendly and will guide you. I hope you have a brilliant time!