My Mum also has limited mobility and has a wheelchair that she absolutely hates using unless absolutely ordered to by her doctor.
I think you need to understand a bit more about what it is like to be in a wheelchair. Her reluctance to use a wheelchair is not just pride it is genuinely unpleasant and a bit scary.
You have no control when in a wheelchair being pushed by someone else you have to trust them entirely. You might not feel safe, especially not on ramps or steep inclines or over uneven ground. You are dependent upon them in terms of direction, speed and route.
She probably feels a nuisance and a burden being pushed in a wheelchair that can't go everywhere.
People treat wheelchair users differently, I have lost count of the times my Mum has been ignored and shop/cafe staff talk over her head to me.
Then there is the disapproval and judgement if you get out of your chair, which has to be weighed against the inconvenience of being unable to reach stuff or fit places.
The people who feel they can make enquiries about your health/medical history.
The chair may not be very comfortable, she may get back or hip pain sitting in it. She may get cold easily.
Mobility scooters are scary if you haven't used one before, and they differ so you have to deal with getting to know it every time. They also aren't suitable for everyone, my Mum struggles as she is short and can't sit at the back of the seat and reach the handlebars.
Please try to be a bit more understanding.
In terms of what we do, does she have a blue badge? That made a huge difference in terms of what my Mum could do as being able to park close by means she can use her limited walking distance for enjoyable stuff. When she didn't we used parent and child spaces sometimes, other times we dropped her off by the door and went to park, we also phoned venues and asked if they had "accessible spaces" or could reserve a space close to the entrance. We had a home made sign for the car to try and avoid any grief about using parent spaces.
In terms of suggestions the national trust are pretty good at having accessible parking spaces, and golf cart transport for those with limited mobility. They often have chairs available to rest in too and the staff and volunteers are very helpful. You can easily spend a day slowly making your way round a national trust venue with lots of stops on a bench to enjoy the view. They have good advance information about the sites too.
Museums and art galleries normally have good disabled access, nice smooth floors, lifts and plenty of seats. Theatres and cinemas normally have accessible seating too.
Would she be happy to sit on a bench for a bit and enjoy the view while you walk a bit further? My Mum goes equipped with a book and an MP3 player and quite enjoys sitting on a bench with a view or even in the car on the seafront while we walk further than she can manage. A folding chair or stool can help with this too.
A scenic drive with lots of short stops to have a little walk or a cup of tea.
A picnic on the beach or in the countryside would work as long as you could park reasonably close.
Is there a preservation railway nearby? A scenic trip on a steam train would not require much walking and normally there is a cafe at either end.