Any county with a population of two hundred ten thousand or more may contract with any city or cities within such county for the financing, erection, ownership, use, lease, operation, control or maintenance of any building or buildings, including open spaces, off-street parking facilities for the use of county and city employees and persons doing business with such county or city, plazas and other improvements incident thereto, for county or city, or combined county-city, or other public use. Property for such buildings and related improvements may be acquired by either such county or city or by both by lease, purchase, donation, exchange, and/or gift or by eminent domain in the manner provided by law for the exercise of such power by counties and cities respectively and any property acquired hereunder, together with the improvements thereon, may be sold, exchanged or leased, as the interests of said county, city or cities may from time to time require.