It does not seem likely that it would jeopardize your federal income tax exemption.  In general, lease or rental of real estate without providing special services or significant personal property is not considered unrelated business income subject to tax, so long as the real estate is not subject to acquisition indebtedness and so long as the rent is not based on the income or profit of the tenant.  Therefore, if your property is not mortgaged and you have a fixed rental (perhaps subject to cost of living increases), rental income from a lease of space on the roof should not be subject to unrelated business income tax (“UBIT”).

You should be aware, however, that the IRS is concerned about such leases, and actually revoked a private letter ruling declaring rent from an antenna tower to be exempt from UBIT.  In the revised ruling, the IRS took the position that rental of space on a tower was not the rental of real estate and the income was therefore subject to UBIT.  Consult with a lawyer about the specifics of your situation, but if you are merely renting space on the roof so that the City can install its equipment, that would probably qualify as rental of real estate.

Even if the rental is subject to UBIT, so long as it is not a substantial part of your total income (and it doesn’t sound like it would be substantial in light of your other activities), it is not likely to jeopardize your exempt status.  Your lawyer can help you on this issue as well.  (See Ready Reference Page:  “Nonprofits Often Worry About UBIT”)

As for local real estate tax exemption, you may find that you are subject to real estate tax, at least on the part of your property that would not be being used for charitable purposes.  Including a clause in your lease requiring the tenant to pay any real estate tax that may become due because of the lease will probably minimize that risk.