Question: In my story, there is a character that is capable of using magic or an ability that allows them to "teleport" as long as they are in contact with the ground or the area that they want to use it on with at least one hand.

For example, in the middle of a circular arena 100m in diameter, as long as they are touching the floor (with a hand), they can teleport anywhere as long as it is "connected" or still physically part of the arena (which means that any floating rocks won't count, and they wouldn't be able to use it to get away from the arena in the case that it is floating).

What limitations can be set on it to avoid being too powerful, and with limitations in mind (or not), what would be the best type of magic/ability to use with it? (disregarding earth magic/manipulation)

My thoughts were to limit it to 75-100m and only usable every second or two, and to be used with wind magic mainly (if mist or fog can be made using wind magic).

Answer: 
Do a little twist on some old thaumaturgy tropes.

You want it to be contiguous floor or some such, so make it where a change in flooring would be a block. Tile floor acts as one piece, wood another. This sets up people who are aware of the ability to build in some limitations. If you can teleport, it's less effective if you can only do it in a two foot square because of the decorative pattern of wood, saltillo and wood tile. This is because there is no connection between the kinds of floor, so the thaumaturgical connection wouldn't work.

Another limitation could be with the cool down and cast times. If your guy has to wait 10 seconds to teleport, or it takes 10 seconds to cast and requires focus to do so, then that makes it less effective combat tool. 10 seconds is a very long time in a fight.
### "Electrical magic"-based teleportation: requires a conductive path.

Suppose your teleportation magic makes your teleporting person act as a self-propelled surge of electrons. As long as they are in physical contact with a conductive surface or conduit, they can teleport to any other point on it with enough space for them to materialize at the other side.

This would impose pretty strong limitations on general use.

* Most dirt/rock/concrete and other surfaces one could stand on would not be immediately usable.
* Bodies of water and wet surfaces (eg. during/after rain) would be easily traversable.
* In urban settings, perhaps a likely use would be teleporting around the electrical grid between points of exposed wiring.
* To use it in non-conducting settings, the teleporter would probably carry coils of wire with throwable weights or a grapnel gun, or perhaps something that splashes water, to deploy in the field.

If you want to impose limitations based on frequency, you can consider heat generated by the teleporter's passage through the medium. If they teleport across a thin film of water on pavement, perhaps the heat of their passage would evaporate too much water for them to take the same path back. If they teleport through a normal circuit in a suburban home, perhaps they'd set off the breaker and not be able to go back through that line.

Related to this, you could add a limitation that they must know, ahead of time, where they are going to rematerialize. Perhaps in electron-surge form, they cannot perceive the world outside of their conductive conduit--at risk of death or severe injury, they must be certain they are re-materializing in a place with sufficient room for their body.