Thats a nice enclosed backyard u have. I would do the following things:

1) clean up the mess

2) Fill the entire scene with granite gravel

3) Add three rocks in a irregular pattern. Recommend rocks about 40 x 80 cm and bigger.

4) Its shady in your area so moss would like it there. Try and add moss around your three mountains (to represent plains...). Then slightly to the right of the stone grouping add a bamboo plant. About 2 meters in height. SHouldnt be too expensive and grow fast. Then whenever u have the money, add a kasuga lantern to the left. Also if there is room try to add an acer palmatum clos to the lantern. And if u can find them, add a few ferns around the rocks. In nature they grow around the rocks, try to recreate that growing pattern.

Then add all your tables and chairs so you can sit and have a nice morning coffee and look at your small miniature island of mountains, forrests and a beacon (the lantern).

Im lousy with photoshop, otherwise I could sketch something for you. Perhaps someone else here can make a nice design?

Remember, dont crowd it with stuff. Thats not what japanese gardening is about. Everything should have a purpose. Bamboo fence around it would look nice too.

This is how I would solve the problem. The hardest thing will probably be to find the stones. remember dont choose round rowks with nice colors (like limestone), go into the deep forrest in the shaded areas and find some old grey edgy stones. And ask the owner of the land before removing them. Three stones of different size should be adequate. Search on the web for "sanzon" stone groupings... The biggest u probably need 3 or more ppl to lift and some equipment. Stone collection is difficult. And hurts ya back :) Please ask if u have more questions.

Remember, LESS IS MORE...
/Henrik

Thanks for the response Henrik.
I need to edit my post to say Japanes "inp
Where would you suggest the 3 rocks to be put? I would definitely not be able to put 3 "real" rocks, but could maybe do "fake/faux" boulder rock...I do like the idea of Bamboo plants, which I would use in a container. I was thinking of tacking on bamboo looking rugs to the fence next yr (the Landlord will be replacing the rotted fence wood panel).
Although easy, I do not think using gravel entirely would work for me. I'd like a little more "flair" in the flooring. Something to break up the areas a bit more...

I agree with Henrik that less is more!

However I have to disagree with what he has in mind.
Your space is very limited. I would forgo any living plants
at all. The point of your space is to create a comfortable
and COOL SPOT to entertain.
Because the property is not yours and you only have a few bucks to spare I think that the best thing to do is to consider using indoor/outdoor carpeting, get some paint and recondition the furniture. Check out furniture at places that sell furniture for nomads or that sell futons. Your idea of using hangings on those horrible fences is perfect.
There are a host of things you can use to cover them up but
first get the idea on what kind of presentation you want.
You indicated an Indian (from India) motif. I think that would be preferred over Japanese as Japanese can be more formal than Indian. Again check out places that sell futons (on the net) and in NYC-you should be able to find some very hip ones there-maybe in the Village??? If you use plants use artificial plants that you can take with you.
If you wish a focus I would look into a small fire pit as it is cool to sit around in a comfortable chair with your feet up chatting with mates munching out and watching the embers glow as you sip your fav brew! Am I reading you right? With only $300 you will have to use your imagination on redecorating what you have to fit the idea that you will come up with so take your time. Maybe work it all out what you really want and start planning on doing it over the course of the next couple of years. From my perspective what is most important is the comfort of sitting so check out those futon places as they will have cool furniture that just might fit your budget or at least give you ideas on how you can modify what you have-either through rebuilding or through painting or ???
And share what you do as I would like to see what you come up with!! Cheers.

Click here to visit one of many futon stores on the net

Forget the oriental and indian or japanese furniture!!!!!
cost is prohibitive. Think nomad or futon!!

I also love the potential this place has. I would look at the furniture, and save out a couple chairs, and a love seat/bench, and a table or two and dump the rest. I would have seating for not more than 6,but for that size place, probably 4. then you can pull out some of your kitchen or dining room chairs if you have more guests. when you decide what you want, take it all out of there and clean everything. rake, sweep, scrub. toss every thing that is not usefull or lovely. mend the fence as best you can. I had an ugly fence that I covered with abunch of rolls of 6 foot tall split bamboo matting, about 50$ for 15 ft long, not cheep, but really lovely cool, and tidy looking. then Id pull all the furniture in from the edges and group it in a conversation area IN THE CENTER!!! get it off the edges, make a nice little water spot in one corner, in an urn or a plastic cement mixing tub that you disguise by surrounding with cement blocks capped with some other cement paver, or something, and cluser pots of small ferns and hostas and stuff all around/behind it, so the cement doesnt show, and get the smallest "little Giant pump you can afford, or go to walmat and get a cheep aquarium pump to get that drip/splash sound, then a few more special plants that you like alot, because you cant have many, In pots of course, and they need to be perennials in your climate, I dont know what that would be, you should go to a nursery, but I think that can be a little jewel box, lastly get some twinkly out door lights this next holliday season at walmart or target, (lots cheeper than "Garden boutiques" and buy some pretty mats and table covers, etc at yard sales or what ever,and some nice little things like iron art grill work, or? to hang on the walls. go to the book store and look at what they haveon "Garden Rooms" in the magazine section in the high end gareden 'zine. you can just browse, and get lots of great ideas with out buying them. hope this helps, have lots of fun.

Wonder what you have done with your space. I liked Henrik's ideas. You definitely want something green and living. You could use pallets or preferably more of the 2 by 2 wood squares I see to raise the seating area. Your fence is not half bad. You can always add oriental plaques, etc as thay come on sale.