How to harvest my Tomato and Cherry Plant

Yes. In the public garden area of the starter (cheapest houses) neighborhood of Oasis Springs. One thing I have observed about the game's behavior. The first time you visit a neighborhood nothing is in the harvest state. You will have to make an initial visit just to get plants growing.

If you play multiple households, put one in that neighborhood and play it occasionally -- I've found that helps develop both the wild plants and spawners.