First everyone may have their own preferences so you may not be able to please all your neighbours, but I'm under the impression that most are happy if they have something to tap when they visit your town and you visit them regularly during events.
Here's a few basics:
1. Leave some items untapped: If you tap everything in your town your friends won't be able to tap anything until the timer resets on that item. I leave several items untapped that have quick timers (brown houses, kwiki marts etc.) at all times for neighbours, and try to leave items untapped at my landing zone.
2. Clear handshakes: Once a neighbour visits you and taps a building, no one will be able to tap the item until you clear the handshake. This is most likely why you couldn't tap some cannons, they were already tapped and waiting to be cleared.
3. Visit neighbours regularly: Everyone has their own criteria for removing neighbours, if you never visit, some will remove you. Some don't care as they have enough cash, FPs etc. and are more concerned with events though. I try to tap buildings with longer timers and try to stay in the same area so my neighbour doesn't have to hunt for my taps. Keep in mind that when you tap a building, you've reset the timer and the same goes for a neighbour tapping in your town.
4. Training walls: Consider hiding some of these behind buildings to keep your righteousness rating up. This is a flaky one that sometimes drops out of nowhere but it's partly due to graffiti. If you graffiti your neighbour it may drop this rating for them and same if they graffiti you. Cleaning it up in your town helps boost it up but since it's a bit unpredictable, most will hide training walls to stop it from fluctuating.