What account will I use for grant income

It's a little confusing because your title mentions "grant income", but your detailed question it sounds more like you're asking about recording money you pay to the city as a from or assurance of some sort, which isn't income.

For that money I'd use an asset account, as the city owes the money back to you at some point.  Then when you get it back and deposit the money, use the same asset account.