There are actually 2 Protea Hotels, and the smaller one at Leadway is nice and friendly with good food and a quiet location. I think the pool area and the tiki hut style poolside bar at the Sheraton is n icer, but food at the Protea Ikeja is better and the hotel is much more modern.
The Westown Hotel, behind the Sheraton is not too bad, though the rooms are a bit small. However, you can walk there from the Sheraton (not advised at night) and their rooftop restaurant, next to the small swimming pool has nice views and serves reasonable Thai and Chinese food.
Heading over the other way, there are 2 hotels, The Ibis Lagos Airport Hotel is okay for a couple of nights, though a bit soul-less. If you want really close to the airport there's the Blue Lodge Guest House, right on Murtala Mohammed Way, next to the Catholic Church (which was originally built for visitors to the church). It's a small boutique hotel and literally only about a 2 minute drive from the airport.
Also on the GRA in Ikeja, in the same street as the Protea, is the Savoy Suites. It's quite small and tends to go up and down a bit. House J on GRA used to be quite nice, though I haven't visited there for a while.
The Welcome Centre Hotel is also quite close to the airport, almost opposite the Ibis and with friendly staff.
Overall, I'd go for one of the hotels on or near the Ikeja GRA, either of the Proteas or the Sheraton and there are plenty of places nearby on the GRA for alternative eating or drinking, though, like most places frequented by expats they tend to be quite expensive.