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With Mobility-as-a-Service platforms moving toward vertical service expansion, we propose a destination recommender system for Mobility-on-Demand (MOD) services that explicitly considers dynamic vehicle routing constraints as a form of a ``physical internet search engine''. It incorporates a routing algorithm to build vehicle routes and an upper confidence bound based algorithm for a generalized linear contextual bandit algorithm to identify alternatives which are acceptable to passengers. As a contextual bandit algorithm, the added context from the routing subproblem makes it unclear how effective learning is under such circumstances. We propose a new simulation experimental framework to evaluate the impact of adding the routing constraints to the destination recommender algorithm. The proposed algorithm is first tested on a 7 by 7 grid network and performs better than benchmarks that include random alternatives, selecting the highest rating, or selecting the destination with the smallest vehicle routing cost increase. The RecoMOD algorithm also reduces average increases in vehicle travel costs compared to using random or highest rating recommendation. Its application to Manhattan dataset with ratings for 1,012 destinations reveals that a higher customer arrival rate and faster vehicle speeds lead to better acceptance rates. While these two results sound contradictory, they provide important managerial insights for MOD operators.