Entrance...note the Cruise ship trolleys that bring you to the site. You can walk to El Morro if you're fit, don't let them tell you any different. It's a nice walk!
So I've had some people ask about specific recommendations around San Juan, and a few about El Morro. El Morro is a large fort in Old San Juan that "back in the day" guarded the entrance to Old San Juan bay. You can read about El Morro in wikipedia, but I highly recommend the video below.
So should you go to El Morro while in Old San Juan? The answer is a bit complicated. I will say that Yes, you should go to El Morro site. There are a few reasons for this. This section of Old San Juan is beautiful, you will see a lot of great views, there is a terrific sunset, and lots of people fly kites and picnic in front of the fort. It's definitely part of the Old San Juan experience.
I personally would also pay the $5 admission to go inside the fort because:
1. I am interested in the history of Puerto Rico
2. $5 is not a bad price and it goes towards the maintenance of the fort and grounds
3. public bathrooms.
That being said, it could take you quite some time to walk around the entire inside of the fort and, if you aren't a big history buff, you might be a little disappointed. So if you're low on funds or time, you can't tolerate school field trip groups, or you don't care much for history, I would pass on actually entering the fort. You can still get a lot of the El Morro experience without actually going inside.
Timeline of events at El Morro
A guy who is WAY excited about El Morro (video)