A friend and I recently stayed 5 nights at the Shaftsbury Apartments in the Harehills area of Leeds and thoroughly enjoyed our time. The apartment is actually a house with a separate basement flat - we only rented the house, which can sleep up to five people. On the ground floor is an open-plan kitchen/diner and living room with a HUGE sofa and smart tv with Netflix etc. On the first floor is a bedroom with 3 single beds and a bathroom with bath and separate shower. Up another flight of stairs is an attic double-bedroom and a second toilet. All the facilities available (fridge, cooker, washing machine, microwave) were in good order and the property was clean and well presented. Dean (landlord) made sure that we had access when we arrived and was very keen to make sure we were comfortable and had everything we needed.
The apartments are close to the A64 York road, which makes them ideal if you want to get out and about but it is either a car trip or bus ride if you want to get into Leeds. We drove to the (excellent) park and ride but there are plenty of buses along York Rd which run into the city. Nearby is also an Asda supermarket and plenty of takeaways with a good choice of different types of food. Parking is on-street, we were always able to park right outside the house so taking luggage in/out wasn't a problem. The only thing I would call out is that the stairs are quite steep so take take when going up/down with bags etc.