sightseeing

On our first day in Rome, we made some sightseeing.
On our first day in Rome, we went sightseeing.
On our first day in Rome, we did some sightseeing.

For many activities, we normally use go + -ing: ‘go sightseeing’, ‘go shopping’, ‘go swimming’.

We can also use do with some sightseeing: ‘We did some sightseeing in Rome.’ Do not use make with sightseeing.

Sightsee is also a verb, so ‘We went to sightsee around the city’ is possible. However, go sightseeing is much more common and natural.