Just a suggestion: I am a die-hard Royal Caribbean'er but did stay in San Juan for 3 days/2 nights precruise last November.
I bought a book called Frommers Caribbean Ports of Call at my local bookstore and it has soooo much info in it about all the port of the Caribbean..... easily worth the $14.95 I paid for it.
In the San Juan section there is a VERY detailed walking tour you can do on your own..... it has maps and tells you where to start, where to turn right etc.... takes about 2 hrs depending on how long you stay at each site..... has info about each place as well as where to shop, where to eat etc etc etc....
Old San Juan is only about 15 square blocks so it is very do-able on your own. Better yet just take a taxi to El Morro and tour it first then walk your way down thru old town.
To do both (old SJ and El Yunque) in one day would be ALOT....
NEXT: 4/27 Celebrity Reflection 11 night Eastern Med
So far: 10 cruises - 5 Royal Caribbean, 3 Celebrity, 1 Princess & 1 Holland America
Life is short ..forgive quickly, kiss slowly, love truly, laugh uncontrollably... and never regret anything that made you smile