I literally just finished this trip yesterday (8 days in Tokyo, 2 in Kyoto, 4 in Osaka). I would say include Kyoto but Osaka is probably optional. Osaka is a great base for other places in the area, but it's mostly like a quieter, slightly less convenient version of Tokyo so you won't get much more out of Osaka itself that you couldn't get in Tokyo. For 9 days, I would recommend 6-7 in Tokyo and 2-3 in Kyoto. There's just so much to do in Tokyo, especially for a first timer. But keep in mind travel time. It's 2.5 hours from Tokyo to Kyoto on the shinkansen, so you possibly waste the good part of a day just traveling between the two cities.
To follow up, here's an example itinerary for a 9 day Tokyo/Kyoto trip for first timers based on what we did (days not necessarily in any order):
Day 1 Tokyo: Ueno Park/Asakusa Day 2 Tokyo: Tsukiji Market/Ginza/Akihabara Day 3 Tokyo: Day trip to Mt. Fuji/Hakone Day 4 Tokyo: Harajuku/Meiji Shrine/Shibuya Day 5 Tokyo: Shinjuku Day 6 Tokyo: Odaiba (teamLab Borderless is a must-see here) Day 7: Last minute Tokyo stuff + travel to Kyoto Day 8 Kyoto: Fushimi Inari/Gion Day 9 Kyoto: Arashiyama
I just did this exact route a few weeks ago, also include Nara if you like animals, beautiful temple and you can pet the deer, also has one of the best ramen restaurants of all time. Kyoto for me was eh, Osaka was lovely, toyko was outstanding.