I would honestly like to see the stats of this year versus the stats of the previous year. Passively, we are trying to make the site of better quality by solving meta issues and creating more ways to improve the site in general (better posts, chat etiquette, new moderators, etc.). The goal at the end is clearly to be better as a whole, as a community and to improve upon our mistakes.
This would be possible with a breakdown of stats from this year and the previous year and comparing them to see how we did. The statistics should at least contain:
- Number of closed questions
The less the better since it means that users are getting the hang of the scope and rules within the site.
More users means more traffic and that's always good. This means that the posts are reaching Google and any advertisement ideas (social media, SE ads) are currently working.
- Flags approved, declined, disputed
More flags approved is bittersweet. At least you know that the users are figuring out what's allowed and what's not but the OP's of the flagged posts are probably less informed on the situation. Less declined flags are better since that means the appropriate usage of flags has risen. Less disputed flags mean that issues in meta are being cleared and important issues are being solved.
- Basic Area 51 stats (top users, questions per day, answer ratio, questions answered, visits per day)
The amount of avid users is quite important since they are the current role models of the sites (excluding moderators who might also be an avid user). The more there are, the more users there are that actually understand the site and can help maintain the site. More questions per day is technically better (if they are well-received) since there is more activity on the site. A higher answer-to-question ration is clearly better since it can help future readers with multiple solutions to choose from. Of course, a higher amount of visits per day means more activity.
The statistics should also include those mentioned in other answers. Answer to be steadily expanded...