Hi! Ive been at Columbia for another program and Ive lived in some of this housing or at least visited and Ill give you my impressions.
Bard housing -- Single room comes furnished with a twin bed, desk, and dresser. Some rooms have sinks some dont. You share the bathroom with your floor and its the cheapest option. Kind of like dorm living but you don't share the room with anyone.
Towers- its either couples housing (1 bedroom) or sharing an apartment (2 bedroom or 3 bedroom). You would have your own room and each room can fit at least a full bed. I feel the rooms are large, the kitchen is spacious, and the bathroom is private. The views of the Hudson are incredible. They do offer single studios in Towers but they are expensive (nice though! You get a full sized kitchen, bathroom, a lot of storage)
154 Haven- These studios are tiny and its the furthest walk from Mailman. They have a kitchenette (no oven). You have your own bathroom. I honestly did not like these rooms and how they were set up. However, if you absolutely do not want to share a space with someone, want your own bathroom, and need the cheapest on campus studio, this would be your best bet. Everyone I knew that had lived at 154 has moved out. Its not very homey or spacious.
Georgian-- Ive only visited studious here but theyre nice. Full kitchen and bathroom. Right across from Columbia Presbyterian and closest to the subway. Downside to this is you will hear the sirens from the ambulances often. Theyre pricier than 154 Studios but cheaper than studios at Towers.
You definitely could find a cheaper option in the Heights but the upside of campus housing is having security/doorman and someone who can accept packages for you.