We did the Narrows as a day hike - it was wonderful, and not that strenuous. My partner wore old tennis shoes, I wore old cloth hiking boots that I didn't mind ruining (they weren't ruined, just soggy after). We used poles, which were very helpful at times (if I recall correctly, this was before we got hiking poles so we just used cheap PVC pipe!).
Orderville Canyon is a side trip you can take near the bottom of the Narrows, it's much narrower and really amazing - don't pass it up!
Angel's Landing and another trip across the canyon from that were also great day hikes. We'd planned on going on the Subway trip also, but didn't get there.
If you have limited time and can do the Narrows in one day, I'd recommend doing that so you can do some other trips too.