This search is extremely fast, and can give you basic info about sourcetypes
| metadata type=sourcetypes index=euc
You can also run this search with type=hosts and type=sources. You could create a dashboard with 3 panels and have one search in each panel. The recentTime in the result is the latest time that Splunk indexed data from that sourcetype (or host or source). The lastTime is the timestamp of the most recent event. In large environments, the metadata command might not be completely accurate, though. This command will look back as many days as it can.
For the complete listing (which you could use the check the accuracy of the above technique), I would do this
| stats latest(_time) as latestTime by host sourcetype source
| eval latestTime=strftime(latestTime,"%x %X")
Since you are only looking at one index, the metadata command will probably be accurate.