I went twice to alpha hotel next to onomichi station (not shin-onomichi). It's a cheap business hotel, and a ok place to stay.
The last time, went to fujihostel (http://nora-t.p-kit.com/page198230.html) as it's even cheaper, it was nice and brand new in 2012. There was not many people, but you never know, you migh have to share the room with other people like in any dormitory room in youth hostel. Anyway, it was a good place.
As for the places to visit, Onomichi in itself is out off the beaten path. Of course you have to start from around Onomichi station (no shin-onomichi), and I would suggest paying 200yen for the stamp rally booklet at the tourist info booth at the station http://www.ononavi.jp/sightseeing/event/detail.html?detail_id=296 it will bring you to a lot of temples and most of the places you have to go. When I did it in 2011, it also included some stamps in Setoda, so you'll have to take the bus or a boat... or by bike if cycling the shimanami... but that migh be a bit off course.
Be sure to go back to omonichi station to claim a prize (usually require something like 5 stamps out of the 50), I got nice post cart and the amazement of the ladies at the counter (I did all the stamps including the setoda one, I guess it's not every day that a gaijin complete it).
An other option is the seven temples "pilgrimage", the stamp rally also bring you there, but in this course, you can get the stamps and a hanging scroll for them (800 yen for the booklet and 300 yen for the stamps) or get the beeds for 500yen each and 300 yen for the string to complete it.
If you read french, i wrote a bit about onomichi in my blog when I went, just search for onomichi. feel free to comment : http://second-time-gaijin.blogspot.com/