The current footprint would probably make the most sense, if only because space for a new site on that side of Burdett Ave seems to be limited (although there is space north of the football stadium, toward Detroit Ave).
In hindsight, it seems a new Field House could have been wrapped in as part of the overall ECAV project - a whole new complex for football, basketball, and hockey. Maybe that was cost-prohibitive or just not feasible at the time (2007-9).
If the current footprint is utilized, then an alternate site will have to be identified - for at least one season. When UNH built the Whittemore Center to replace Snively Arena (a true "barn" in every sense of the word) in the mid-90s, they split "home" games between a municipal rink in Manchester, NH and what was then the Cumberland County Civic Center in Portland, ME (approx. an hour from Durham). For HFH, any alternate site would need a decent amount of seating, so that eliminates many of the smaller local rinks (Frear Park, Albany County Hockey Facility, etc). MVP Arena comes to mind as a possibility.