There is no lack of places to stay near El Yunque all year long. Remember there is no winter in Puerto Rico - only a nearby hurricane will close the park. See the main links page for NOAA hurricane center - the danger is mostly in September. The last major Huricane was Maria in 9/20/2017 and the park was closed for over a year. The La Mina trail and fall are still closed. The big issue is how you get to the park - with your own car or in some bus or limo service. It's your choice. You can also use a guided tour the 1st day, then come on your own the next few days.
Note: be wary of web sites and information posted before Hurricane Maria, some hotels are in repair, some have closed, some are old and do not mention PR-66 etc. Many web sites are not be informed of the closed sections of El Yunque after Maria and the closed hotels around it, some do not even know about PR 66.
View from El Morro in Old San Juan - 2 hrs from El Yunque via PR 66
There are several aspects to lodging to access the EYNF park:
1) It can be very near, within forest but exclusive - need early reservation and are expensive and few. This is because the forest does not always end with the park. There are many lands next to it that have preserved their forests and have rivers and trails. Examples are in the bottom of the page - some are awesome in all respects, some are ok but simply close to the park or the forest.
2) It can be a hotel nearby in the Luquillo area - near both heavens: El Yunque and Luquillo beach. You can even camp out in Luquillo beach for a fee.
3) It can also be in San Juan hotels and travel here daily - see my blogs about this - since there I assume you travel to/from San Juan for brevity. For this we assume you use toll-Route PR 66 to get early to the park and in comfort.
4) And for the wealthy or with spare cash that want a top class lifestyle there are incredible resorts around the forest in strategic locations with many rooms. Another newer example is Palmas del Mar complex with direct access to Rio Sabana park and the islands. There are air links from San Juan too and we are also close to the Virgin Islands: Vieques air link
There are two major Islands close to EYNF: Vieques and Culebra.
Note: I tried give direct links for the sites as possible - smaller places at the end.
Major Luxury Hotels Near El Yunque rainforest and the beach:
Close to Rio Sabana Park - El Yunque, Luquillo
A few Villas in the forest near El Yunque - wip:
Awesome Yuquyi Tree Houses - Rio Grande (picture above)