There are two main places worth visiting outside of the Prophet's Mosque in Madina; this is one of them (and the other is the Hejaz Railway Museum).
Take an Uber here if you want to avoid being scammed by the local taxi drivers or want to avoid haggling. It cost us 15 Riyals one way.
The museum has some really interesting models and artefacts. They offer tours but depending on which day and time you arrive they may only have some running, and in only specific languages. When we visited they only had an Urdu tour that afternoon so it may be best to ring beforehand.
The history of the city is laid out very well, documenting the landscape, the people and how it's been shaped over the years. One of the most interesting parts of the tour was the evolution of the Prophet's Mosque from a house, courtyard and home to the massive complex it is now.
When so little history and culture is missing from the Saudi cities, it's nice to see them showing some responsibility in preserving and sharing history.
Outside the museum entrance is an artist calligrapher, a fine art in the islamic world. He does some great work and will write any name onto a framed board as a souvenir - worth it as this is a dying art I suspect!