Overnight stay at an Onsen Ryokan Hakone

Hi all, me and a couple of friends (4 total) are visiting Japan at the end of the year, and have decided on an overnight stay in an Onsen Ryokan at Hakone.

It's the first time in Japan for most of us, so we have no idea where to start, and was just looking for some suggestion.

Our budget is around 20,000 yen pp. for a single room, and if possible to include meal(s).

We do also have one question that is a concern for us. 3 of us have very visible tattoos (sleeves, back and chest) pieces, so covering up is not possible. We know that we won't be able to use ANY public onsen. But was wondering if our tattoos would be of any issues if we booked a private onsen during our stay (I don't suppose it would be?).

Also would it be possible to get a private onsen with a view/outdoor one? or is that out of our budget?

Sorry, I've tried using search engines like Japanican but every time I've put in the filter searches I get back no results, maybe I'm using it wrong.

Thanks in advance for any help =)

Tattoos would not be an issue if you get a private onsen - either in the form of room with its own bath (expensive) or "rent-to-youself" bath.

By the way, not many hot spring ryokan have "single rooms." I don't know you and your friends' gender, but could you consider 4 of your staying in one room, or 2 and 2?

"By the way, not many hot spring ryokan have "single rooms." I don't know you and your friends' gender, but could you consider 4 of your staying in one room, or 2 and 2?"

Sorry I worded that wrong. We want one room to share. So we have no problem with that.

Have you guys got any recommendations? Ive tried using Japanican to do some searches. But as mentioned everytime i put in the filter for 1 room 4 adults theres no results.