The current study is motivated by the need to better understand the potential impacts that vehicular automation may have on individual decisions of residential and work relocation in a future autonomous vehicle (AV) scenario. The study employs a multivariate approach to model five behavioral dimensions simultaneously: (1) technology-savviness (TS) propensity, (2) interest in productive use of travel time (IPTT) propensity, (3) interest in work relocation, (4) interest in residential relocation, and (5) tolerance to an increase in commute travel time. Data from a web-based survey of commuters in 2017 in the Dallas-Fort Worth Metropolitan Area (DFW) is employed. The results show that both TS and IPTT, as well as demographic variables, impact relocation decisions when individuals have a private AV available for their commute. Importantly, there is considerable heterogeneity across individuals in the willingness to relocate and/or accept longer commute times in an AV future. As such, our model results may be used to inform inputs to land use and travel demand models in an AV future. Also, our results suggest that the magnitude of value of travel time savings (VTTS) decrease considered in many earlier AV impact simulation studies may be much higher than reality. Relative to 50% and even 100% VTTS decreases assumed in many studies, our results suggest a much more modest 30% or so overall decrease in VTTS because of the ability to commute in a privately-owned AV. Finally, our results do predict a rather substantial extent of urban sprawl due to AVs, potentially up to a 68% increase in the horizontal spread of cities such as Dallas-Fort Worth, unless proactive planning and policies are implemented to avert such consequences of AVs.