There’s two main hotels I would suggest:

The Hilton is just a few mins cab ride from Pinks and the Campanile hotel bar, guests services at the hotel can organise a cab for you, or simple use Uber, perhaps cab share to spread the cost ? The Hotel sits within MK doms football ground, and a high end hotel, rooms come with a fridge and some with a mini bar.

The Campanile is literally across the road from Pinks, this is a budget hotel so no frills but ticks the box for location.

Hilton Double tree

Campanile (opposite pinks)