Train passes for 10-day trip

I will be travelling to Japan for 10 days with first 2 days in Tokyo, 4 days based in Osaka with trips to Kyoto and then final 3 days in Tokyo including day trip to Yokohama. I will be flying in/out of Haneda

I was thinking of getting the 7 day JR pass to start on the day I travel to Osaka but means for the 2 first 2 days and last day the pass will not be active.

I was thinking of therefore getting the SUICA card to use on these days but wondered - is this the best option?

Can the SUICA card also be used on trains/subway in Osaka and Kyoto?

Yes, a Suica Card can be used in Kyoto and Osaka. It's just an IC card and Suica means it is JR East branded.

As long as the Welcome Card is still on offer, the Welcome Suica Card:
https://www.jreast.co.jp/multi/en/welcomesuica/welcomesuica.html

Is great for foreigners who are not sure if they are ever coming back to Japan and spending under 28 days in Japan because you do not need to pay the 500 yen deposit and can just run the card down to 0 and then keep it. (You can keep a regular Suica, but you do pay a deposit for it.)

It's 6 of one, half dozen of the other on whether a JR Pass is worth it. The travel you are doing in Kansai won't be terribly expensive since most of the time you will probably use a Special Rapid Local train to get between Kyoto Station and Osaka Station (this is of course assuming you are not closest to a Hankyu or Keihan private lines, in which case you might want to use those to get to Osaka.

Good luck!