The pavement is hard on my tires, so I prefer to land in the grass.
It depends on the airfield. Landing on grass is only recommended if the ground is maintained to a reasonable standard and clear of obstructions. Some airfields have grass strips maintained for that purpose, on others the grass has lights, wires and cables, or just lots of holes/ruts which will be far worse than the tarmac.
Some airfields are only grass, tarmac is not a prerequisite for having an airfield.
You want to know before you go, how to find out depends on where you are. There are flight guides and websites in many countries that tell you what is available, but it always makes sense to call ahead and ask the condition of the available grass, and to find out if there are any unofficial grass areas you can use.
There is also ATC, at a towered airfield you must land where you are cleared, you can'd decide to land on the grass nearby because you want to as it's a violation. If there's grass available you need to make sure you ask for it and they will give it to you if they can, most of the time ATC is helpful. If they say no there's probably a good reason. At an untowered airfield it's at your discretion, if there's grass available and it's in decent condition you would state your intention on the frequency and follow normal procedures.
Well, you're using land that is under the authority, or delegated authority, of somebody, so technically you need that authority's permission to use other than a designated landing area under the airport's license. Remember that there could be liability issues for the person responsible for the airport, completely aside from the physical suitability of the area you want to use.
So from a strictly legal/regulatory perspective, you need the authorization of:
At a controlled airport, the delegated authority, ATC.
At a public uncontrolled airport, the delegated authority, the airport manager.
At a private airport, the owner.
In the real world, if you are using the grass at an uncontrolled public airport and you're not getting in anybody's way, you'll probably be fine, but if you land on the adjacent grass and then see a guy marching toward you with steam coming out of his ears, that's probably a manager or owner coming to chew you out because there is a policy against it.
Bottom line: the wise pilot checks with whomever is in charge first, if in doubt.