The Hakone website have many suggestions : http://www.hakone.or.jp/hiking/
I personally would do one of the course going to Owakudani (from 13 to 16) as it's an interesting place. But it's better to have a back up plan if the toxic gas sign is on.
I did 13 as I got there before the ropeway was open, was a nice walk and not too hard for a person not used to hicking and without specialised gear. I was also able to take the ropeway going down for free (I guess they assume you used it to go up).