City investments follow you. Cities function at the building level of the combined investments of all players in the city (If you have 1M In Town Hall, your Town Hall is the level of a 1M investment solo. If you join a city with 1 other player who also has 1M in Town Hall, both of you will have a Town Hall at the level of 2M Investment). If you leave your solo city, it will vanish. If you leave any city with other players, your investments there will downgrade their buildings, and you can either re-create a solo city with your investments, or join a new city under the same circumstances.
There is a 10% tax on city hopping that is reduced by 1% for every 24 hours. This tax is, I assure you completely insignificant at lower levels. It is designed to prevent high level players from hopping around. Make use of the Town Hall for Furniture Upgrades. Upgrade as much as you can. Probably around shopkeeper level 25, you will want to join with other players who have and will continue to produce your same City Investment Rank.
City Trade is a new feature as of August 2016. You can make Requests that each other player can fill. It is limited to 1 slot, per player. There is an 8 hour timer before you can change your Request to a new Request, regardless of whether your Request was filled or not.