Dogo onsen sleep?

Hi,
I wish to go to Matsuyama when visit to Japan and to the onsen of Dogo.
Is it possible to sleep at the onsen or can you recommend any place closeby in the same kind of style?

What policies to tattoos does the bath have?

Since having a small tattoo 1-2 inch wide I might need to cover it up somehow...

While most people think of the Dogo Onsen Honkan when they think of Dogo Onsen, there are many ryokan that make up the greater "Dogo Onsen". You cannot stay overnight in the Honkan, but you can definitely stay in one of the ryokan that are part of the onsen.

To be fair, you could stay anywhere in Matsuyama.
Dogo Onsen is really just a suburb of Matsuyama and can be reached by the city's tram network.
Check it out on a map and you'll see what I mean.
There are modern ryokan and hotels around the Honkan, but you may prefer to stay somewhere cheaper a short ride away and save your cash for a lovely old ryokan elsewhere in your trip...

Dogo Onsen is famously tattoo friendly.

I recommend watching this: https://www.youtube.com/watch?v=r6-t54PfAJQ

All of his vids are pretty good.

Wow lovely video. Very interesting. Thank you.

Say, as I will not be there during summer but in early April, is it still possible or common to wear yukata outside the onsen or would it be too cold?

When visiting Koyasan they offered a yukata as well as the coat thing I forgot the name of... hanten? Could it be found in Dogo as well for use?

By the way, just a bit curious about the pricing. It says you can use the facilities nfor 60 or 80 minutes. Does it mean I must exit the building after 60-80 minutes or only the bath and changing room?
There are relaxation rooms and a museum as well. So it would take some time to visit too.

„Does it mean I must exit the building after 60-80 minutes or only the bath and changing room?

yes.