I live just south of Lincoln and would be happy to join in! A lot of the places uphill and on the High Street are difficult to access by taxi since so much of the centre is pedestrianised but Brayford Wharf North is a possibility.
It's not glamorous but somebody told me that the Curtis Bakery in the High Street, just north of St Marks Street, offers an excellent mug of coffee plus very good value bacon rolls and/or cream cakes in its little coffee shop. That's less than five minutes' walk from the temporary bus station, not much more from the rail station and should still be accessible by taxi ...