PLAIN FORM: 「他の店に行こう．」
POLITE FORM: 「他の店に行きましょう。」
If those kanji were options, the tooltips would even help...
"Chigau" was used as "different" in another sentence. Would it make sense to use it here instead of "Hoka" here?
う is not nececcery, right?
what would the kanji for ほか be here, 他 or 外, or could it be any of them?
The more commonly used one is 他. 外 means outside, even when its read
ほか, so it's mostly only used in expressions like 思いの外. But ほか is actually totally fine in hiragana form also.
So many homonyms in Japanese.