Of course there is a legal answer - and it's been stated so many times now that I despair. In this world individuals have rights - quite a few. They have the option of enforcing them themselves, or using another individual or body to do it for them. I own my music, as do every other composer. You do NOT have the right to use my music unless I, or my agent agree some terms. My music of course is dull, boring and not remotely designed for the masses - but let's assume for a moment that your licence to play TV programmes for the hotel is in force and you are as 'legal' as you think you should be. The BBC, for example, if they use my music will tell PRS and they put a tick in the box for me as the composer of the music. I get paid for writing it. As I also own the recording rights to it, this is controlled by PPL and PRS will pass it on, and I get paid for the use of the recording, which also might mean a payment for the piano player I used, and the drummer? Now the tricky bit. Your TV licence is simply a licence to have in your hotel television receivers, which now is broadened to include internet connected TV. The BBC may well collect the money, and they keep detailed records of the content, but what if you are watching one of the music channels, or an old documentary channel, or even something coming from youtube or facebook. You as the licence holder are paying to have the equipment - you are not paying anything to me, and if one of those programmes has my music in it, how do I get paid? By PRS (and PPL, who you also need to be paying). You probably think this grossly unfair, and I do understand that, but you have no right to use anyone's music without their permission. With apps like Shazzam, identifying music is so easy nowadays, but if we assume you are an ultra keep it legal person, how on earth would anyone pay for the music they use without PRS or PPL? Last month I made the grand total of $5.70 for music used from the net, and my music was streamed in roughly 20 countries, paid at the rate of less than half a cent per play. If I was Robbie Williams I'd make lots, but I'm not. I like the idea of PRS charging you for using music, even though I'll probably never get any of what you pay myself - but others will.
Check the wording of your TV licence and it explains what you are paying for. It doesn't do anything for the music content at all. PRS don't really deal with the public as they complain so much. I don't want them wasting their time on answers that you won't like or agree with. I'd rather they paid it to the artists who earn the money. I walk through Tesco, and there's a little stereo player, playing music. I wonder if they pay for that? I hope so.
You probably have a booze licence. If you sell lots of alcohol and few soft drinks, or vice versa, the licence variable. You also pay VAT on it too, your drinks licence doesn't also cover the VAT. If you take empty bottles to the rubbish dump/recycling plant they too probably charge you - again, the licence doesn't cover disposal.
The legal answer is simple. You cannot use (consume is the proper term) things you don't have rights to - and music is protected in law. It belongs to the person who wrote it, or performed it. Same as photographs or video images, poetry, paintings or anything people dream up in their heads. If you download a picture from the internet, print it out and stick it up on the wall of your hotel you get the same reaction from the owner of the image - that's mine, who said you could use it?