What is your price range and do you do all of your own work already? If it breaks, who fixes it?
From what I've seen, a lot of the bikes that you will buy online will be inferior to better known brands. If it is cheap online, it will be a cheap bike. Better off going to a big box store and buy one of their offerings. I know that Canyon is direct to consumer now and some other places sell name brand bikes but they are really screwing the LBS. Check local cycling clubs or craigslist too.
The reason to say this is that even though the size sounds right, you often don't know without actually putting hands on one. you can get close and that usually works, but to stand over one and feel comfortable is the key factor IMHO.
Not sure why you can't go to a LBS. We have a few LBS around us but my favorite closed its doors a couple of years back. It was like losing a friend. Great people. Great customers. A place to spend a Friday evening over a few cold beers putting parts on a new frame. If it's a distance thing, that's fine.