As spudqueen states, this is primarily a U.K. site, but there are a few of us Yanks that frequent the site. I live in the western U.S.
Generally, you won't see any tax advantages to your question, especially since all U.S. Territories and Possessions, including Puerto Rico, are subject to the same taxes as we are here. Additionally, Puerto Rico's income, sales and assessment taxes can be substantial, depending on the econcomy. You will still be paying U.S. Income Taxes assessed on your U.S. income. You will still be paying property taxes and assessments on the Illinois property... you may wish to contact the Puerto Rican tax authority for clarification. They can be reached at:
Negociado de Asistencia
Contributiva y Legislaci�n
Departmento de Hacienda
P.O. Box 565
San Juan, Puerto Rico 00902-6265
(787) 721-2020, ext. 3611
Best of Luck!