First of all, let's use "食事した/しょくじした" instead of "食べた" because "食べた" requires you to specify what you ate such as breakfast, sushi, fruit, and etc. "食事した” is more general term used for eating/eating out without mentioning a specific thing you ate.
I also ate in Tokyo. (My friend eat in Tokyo: I also ate in Tokyo.) →私も東京で食事した。
I also ate in Tokyo. (I ate in Okasa: I also ate in Tokyo.)→東京でも食事した。
I also ate in Tokyo. (in addition to other activities you did)→東京で食事もした。
I also ate Chinese food in Tokyo (in addition to other food you ate or in addition to other activities you did).
→東京で中華料理も食べた。
I also gave ハンナ a book. (I gave John a book: I also gave ハンナ a book.)→ハンナにも本をあげた。
I also gave ハンナa book. (I gave ハンナa book mark: I also gave her a book.)→ハンナに本もあげた。
Additional information:
"In + place you can visit" = で instead of に as in "in Tokyo" (東京で), "in the movie theater" (映画館で), "in the hospital" (病院で), whereas "in + place you can't visit" = に or 中に(depending on sentences) as in "in the fridge" (冷蔵庫に/冷蔵庫の中に), "in the box" (箱に/箱の中に), and etc.
I hope this helps you.