If this is before end end of September, even early October might be good weather I would check out Ada Ciganlija an easy bus in 15mins or taxi from your hotel 400RSD and Zemun Quay. 20 mins bus or 500RSD taxi.
Take ID if you like bike riding. Hire a bike for the day on Ada and ride around the big lake, explore Ada, ride the river bike tow path back towards the old town, it follows the river, when you get to the big blue bridge with the lift, take the bike up in the lift, cross the bridge and turn back on yourself to the river, follow the tow path to Zemun Quay, lunch on one of the floating pontoons.
if you don't want to long ride bikes, go to both places by taxi. Take a taxi first from your hotel to Hotel Jugolslavia, that's directly on the river facing the pontoons then walk up to old Zemun. That wil be a nice couple of hours stopping for coffe or lunch on the river.
When on Ada take the little train around the big lake and maybe take lunch or early evining food the fishing lake at Ada Safari. :
Back in town, Hotel Moskva is A1 location, can't be better really. You must go see the old quarter Skadarlija by night, it's but a a 10min walk, just ask someone. Here you must take a late dinner one night with local musicians and old ambience, I would suggest the terrace in restaurant Ima Dana offers best quality and value.
For better food and wonderful location, usually some live classic music in background, take dinner on Kalamegdan terrace restaurant. You might be shown it on the tour. The drinks gardens below and above this restaurant have great views across the river confluence, go to the upper garden at sunset for cocktails! Book a table out on the terrace.....lovely.
Have a good time