You can enable logging to multiple lcoations (syslog, console port, vty lines, internal buffer). It sounds like you would like it to go to the internal buffer. Here's an example on how you would do that.
logging on
logging buffered 16000
logging buffered warnings
This would send warnings to the internal buffer. You can then view them with show log
To send the log to a syslog server-
logging trap notification
logging [IP of syslog server]
To enable logs to be seen on the VTY (as they happen)
logging monitor
And on the console port
logging console
Hope that helps
