Is there a way to view only questions that have not yet had a best answer selected?
As Davïd mentioned the Data Explorer is a powerful way to sort through and find things in the content of SE sites. However for this particular case it is overkill, the built in site search has this feature built in. If you do a search you'll notice an "Advanced search tips" panel on the right with some parameters you can add to any of your searches. To find questions without an accepted answer you could search for is:question hasaccepted:no. Given that here are a couple thousand results you'll probably want to narrow your search down with some other parameters, keywords or tags that you're interested in, but that should get you started. The help page on searching has even more tips.
I think the best was is by using the Stack Exchange Data Explorer (SEDE), available from the
data link in the footer to every page on the network. For example:
- this "Orphan questions" query finds Qs with "high votes, high views, not CW nor closed yet without accepted answer" (note that you can sort on columns by clicking their header);
- or find "Unlocked Questions From High Reputation Users Without Accepted Answers";
- or find the top n questions without an accepted answer, where the Q has a score over x;
- ... or roll your own! :)