Think soft things, as you're doing. You might also get a carpet stair runner or carpet pads/rugs that adhere to each step. Some cushions on the bench. Anything you can hang on the wall? A large textile there might help. If there's enough natural light for a tree, that might also contribute to absorbing some noise. When you get some furnishing in, like the bench, maybe a table and upholstered chair, some things on the wall, there will be objects to interrupt some of the vibrations and absorb the noises.

Ditto Squirrel. Short of insulating the walls fabrics and upholstered items and a tapestry to two on the walls should greatly reduce the echos. I'd ask the landlord to get involved with the costs. There's always thrift stores and Craigslist to save on costs.

Plants can also serve to muffle noise. I'm thinking of big tropical plants with lots of fronds.

Yah, what they said. Anything soft, fabric-y, like rugs, tapestries, upholstery, curtains, pillows. The rougher the fabric texture, the better it will absorb sound.

Also books. Do you have room for a bookcase?

The area rug should make a big difference in the amount of perceived noise.