Numberlink

Numberlink is a Nikoli puzzle in which the aim of the game is to match all the number pairs on the grid by connecting them with lines. The game can be played on any sized grid. The difficulty tends to depend on the amount of number pairs and on the available paths between each number path.
A well crafted Numberlink puzzle is one that manages to cover all the cells on its grid with lines and has a unique solution. This isn't a rule however.

Speaking of rules, they are as follows:
- All number pairs must be linked with a continuous, but possibly corner turning line. So a 3 will need to be linked with another 3 through a series of straight lines.
- Lines cannot branch off of each other and they cannot cross each other.
- The numbers must be matched with the two ends of the lines, so drawing a line through a number to cover more cells does not count.

Standard version

Numberlink is a relatively tricky puzzle to solve as there aren't always clear deductions that can be made. Instead you often have to rely on a little trial and error to figure out the right paths. However, there are some deductions you can make in some Numberlink puzzles.
For example, in the example below the 1's and 2's have no choice but to link via the top right corner of the grid, otherwise they'll end up surrounding the 3 in such a way it'll only have a path to the other 3 by going through the entire grid, which in turn blocks of many of the other numbers.
Likewise, the two 7's have no choice but to connect via the bottom right corner or else they'll block the 4, 5 and 6 completely.

Converting it to an RPG setting.

Numberlink provides some fun adaptation opportunities and they don't have to be too similarly themed either. Connecting magical sources, laying down a power grid, connecting towns or islands via unique routes, allowing pairs of lovers to communicate in secret. These are just a few of the possibilities you have at your disposal.

For my example I've gone with a light based puzzle. My character finds herself in a room with 8 pairs of colored light emitting orbs. She's also been given a plentiful supply of mirrors and the instructions on how to solve a Numberlink puzzle. The only twist is that instead of numbers she has to link the lights, which is done by placing down mirrors and allowing the lights to fire in one of four directions (thus creating the connection lines).

As long as she manages to avoid crossing the beams of two lights she'll be fine, even if it means temporarily placing mirrors in the wrong locations, but if she does end up crossing the beams it'll have explosive consequences.
Once she does solve the puzzle the connected lights will trigger an event that'll allow her to move to the next part of the story.

On a final note, this puzzle isn't always ideal for the less puzzle enthusiastic groups. Since the deductions you can make aren't always as clear as in some puzzles, it can become a time consuming process to guide a party through this puzzle.
Creating the puzzle can be tricky as well, at least if you want to stick to the 'all cells covered' guideline. I personally find it easiest to start from the outside. Make sure all the outer cells are covered by lines, then work on the next inward ring and so on. It's often easier to move some of the inner lines around instead of the outer ones, hence this work method.