Regarding JAT, expect the same what you had before, with a few more years added on the planes They did hire a bunch of new cabin crew some time back, so service might be improved.

They also added a few things in BEG: A new bar/restaurant, the main duty-free shop has been somewhat refurbished, and last time I was at the airport, they were redecorating the hallways, removing the ugly dotted rubber (I hope!). Business Club has been recently refurbished, the furniture is spiffing new, it's quite spacious, and has an open bar, and some food IIRC. Really good lounge, IMO.

The aviation museum is great, so I was told several times. I've been planning to visit for years now, but somehow I always manage to get to the airport in the nick of time.

In SJJ, there is actually only one operational lounge (it's quite irrelevant what it's called ) When you get past passport control, just keep walking straight, past the duty free, and on your right there will be the lounge with a manned service desk. Other than the drinks on offer in the lounge, you can get a pretty good espresso, but you need to ask the lounge receptionist. They can also make you a Bosnian coffee

SJJ is quite small indeed, and check-in, security and passport control is a breeze. There is additional quick security check at the gate before you board, but as there are rarely crowds, you can safely be in the lounge until the boarding call, and then walk over to the gate. 45 minutes before departure is more than enough for SJJ. You will probably have time for a morning coffee in the lounge. I'm not sure about JAT, but if you can, check in online and save yourself some time.