For a trip centred on University of Bath, the Skyline and outdoor time, I'd choose the campus side if your accommodation plan supports it; the trail and Prior Park are the natural anchors. For a couples' weekend that also includes the Roman Baths, Abbey, Georgian walk and an evening event, central Bath wins. Its advantage is practical: you spend less of the trip shuttling between separate plans.
The Rose And Crown is the one I'd choose only if the restaurant-and-garden stay is the point; for a city-and-campus mix, I'd keep the map tighter. Browse Bath hotels and apartments while you shape the plan, and pick the base that leaves you more time doing the things you came for. That's how you end up meeting your people, not just passing other travellers in transit.