For regular check-ups and ongoing conditions, consistency and convenience usually matter more than a hospital's overall reputation.
For ongoing or chronic conditions, prioritise a hospital you can realistically get to often without it being a burden. The "best" specialist across town is less useful than a good one you'll actually see consistently.
Ask about specific doctors, not just the hospital. Outpatient experience often depends more on the individual doctor than the hospital brand, it's worth asking around about the specific person you'd be seeing.