The notion that candidates would merely contest places that have the densest populations and/or their strongest areas is nothing short of dense (pun intended).
Candidates would obviously compete in areas where the greatest value ($) per vote could be extracted (which, contrary to popular belief, isn't going to be in expensive California or New York media markets) and in areas where the greatest concentrations of elastic voters exist - which certainly is not going to be in Democratic strongholds. It'd result in candidates targeting media markets (and therefore voters) all over the country, including many places that get zero attention in current presidential campaigns.
It'd be more likely that Democrats would compete nowhere, given that the country has wanted us in 6 out of the past 7 presidential elections, than to confine ourselves to the densest urban areas in a few states.
THIS!
Also, I think you'd see campaigning in way more states. Right now they only campaign in a few key swing states, ignoring most everyone else. Under a PV, every vote in a safe or purple state regardless would be just as valuable. You'd see Dems and Republicans campaign in Alabama, Hawaii, & Kansas along with the usual suspects. Turnout would even out around the country I believe too; turnout right now is slightly higher in swing states than safe ones, and ones like Texas and New York in particular have much lower turnout compared to Ohio, Florida, and Iowa.