I think these meet your criteria but I haven’t checked if they have availability or are doing bookings etc sorry:
Dishoom is a 5 minute walk from Opheem and does drinks and cocktails.
40 St Paul’s in the Jewellery Quarter is a 10 minute walk from Opheem and probably has the most extensive and interesting cocktail menu in the city, but it’s small so may not have the buzz you are looking for. There’s also St Paul’s House nearby that’s bigger and very nice so you could do both.
On Colmore Row which is a bit nicer you have the Alchemist. You could walk there from Opheem.
There’s also Marco Pierre White’s on the top floor of the Cube whixh you’d probably want to get an Uber to which is expensive but within stumbling distance of the Hyatt afterwards. There’s also a couple of places nearby like Aluna and Chez Mal.
If you do want to go out out after, then there are a few bars like the Botanist, Revolution De Cuba, the Lost and Found, Dirty Martini, at Be At One based around Temple Street / New Street.
I’ll carry on thinking and let me know if you have any other questions about places to go