Accomodation in Hakone

I am heading to Tokyo with my girlfriend on 19 Sep and would like to include a 2D/1N trip to Hakone.

I was looking at the options of ryokans/hotels in Hakone and it seems quite pricey.

What is recommended if we would like to stay in Hakone with onsen and preferably below $300 inclusive of a meal?

Lalaca seems popular but they don't have many rooms so you'd better check soon if there still is availability.

The Ichinoyu group of ryokans while not overly fantastic has reasonably priced options, at about 8,000 yen or so per pax with b'fast and dinner included.

Lalaca is really popular with me, and I recommend it every chance I get. I stayed 4 nights and they are really lovely people. I think you'll be out of luck for the weekend, your best chance is to book during week, maybe Monday to Thurs.