Hotel Lawrence is ideally located for tourists at a fraction of the price of other hotels.
Don't worry too much about the stories of sketchy alleys and stairwells. It is true you have to walk 30 meters down a side street to find the stairwell (on the right, small hotel sign at eye level), but it did not seem unsafe. Same with the stairwell: guy sleeping on 1st floor landing, sacks of something blocking much of the stairwell, unpainted wood, but well-lit at night and not apparently unsafe. The hotel staff are professional and helpful. Rooms are basic budget, though cleaner and brighter than average. Bring your own bedsheet and toilet paper. Common bathrooms are scrubbed daily but still budget common bathrooms... except for the lovely surprise of hot water (!) once you figure out how to operate it. The one on the end had the best hot water. Breakfast was decent.
Only downside was the (upscale) dance club across the side street. Bring heavy-duty earplugs, or don't come back to the hotel between 10PM and 1AM. If there were no dance club next door I would have given this hotel a five star.
Even considering the dance club and unattractive exterior, this is a stunning budget value for Mumbai.