We present newly obtained X-ray and radio observations of Tycho's supernova remnant using Chandra and the Karl G. Jansky Very Large Array in 2015 and 2013/14, respectively. When combined with earlier epoch observations by these instruments, we now have time baselines for expansion measurements of the remnant of 12-15 year in the X-rays and 30 year in the radio. The remnant's large angular size allows for proper motion measurements at many locations around the periphery of the blast wave. We find, consistent with earlier measurements, a clear gradient in the expansion velocity of the remnant, despite its round shape. The proper motions on the western and southwestern sides of the remnant are about a factor of two higher than those in the east and northeast. We showed in an earlier work that this is related to an offset of the explosion site from the geometric center of the remnant due to a density gradient in the ISM, and using our refined measurements reported here, we find that this offset is ∼ 23'' towards the northeast. An explosion center offset in such a circular remnant has implications for searches for progenitor companions in other remnants.