Hellobee Boards

Blocks can take up very little space if stored in a box.
Big Magnets on your fridge (or freezer, or dryer, really anything magnetic).
Do you own your space? Paint a section of wall with chalkboard paint and chalk is great. Buy the big sidewalk kind if you're worried about eating it).

@MrsHoneyC: We have a small space too...I would suggest personalized items, like a book with photos of family members, like this one:
https://pinholepress.com/products/mini-book-of-names-faces-85-1-0-01/

Nesting blocks:
http://www.landofnod.com/tower-of-babble/f1247

Or how about a play tent that can be folded up, like to ones at ikea.

My 16 mo old loves anything with doors, to open and close open and close. So if you think you can fit one larger item, how about a low profile kitchen like this:
http://www.amazon.com/Hape-Creative-Cookery-Club-Educo/dp/B000A6L6WK/ref=pd_sim_t_22?ie=UTF8&refRID=0FPDHAQRXR8J7NGC9KV4

What a cute play corner! How about asking for experiences and things to get you out of the house?

sensory play bath toys

An activity table like the one below would get a lot of use. Fill it one day with pasta and scooping toys, take it outside with water another, etc. then cover it up and use daily as a table with chair. LO can play with trains on top or make art projects. It's not cheap, but will get a lot of varied use, and is good bang for the buck. Multipurpose items are best for small spaces.

http://www.amazon.com/gp/aw/d/B000RZO1HQ/ref=mp_s_a_1_14?qid=1414503312&sr=8-14&pi=AC_SX110_SY165_QL70

http://www.amazon.com/gp/aw/d/B0013C844S/ref=mp_s_a_1_10?qid=1414503312&sr=8-10&pi=AC_SX110_SY165_QL70

We have the same size space dedicated in our living area. I asked for books, books, and more books. We also got the little people school bus (bonus: all the people get stored inside) the Barnum Drum (another storage toy) and a pop corn popper to help with walking were the favorites. If people asked for toy suggestions i told them nothing big it should fit in a toy box.