My comment is oddly writen, I think you'll get the idea
Your problem: Location and time of year and time of day when they took them pictures being it your renting or buying.

Solution Mapquest the potentual address of the apt and zoom in on airial views to get a second view of the "shade" even then it's a question of what time is it on what day of year but knowing a sun dial and how they work will help a bit

Apt priority conciderations while viewing these mapquest and renters picture views.

Imagine yourself steping out on the balcony at 7 AM on a mid spring morning and a nice sunny day the sun will be to your left hand side as soon as you open the door. Your in balcony garden heaven. As it moves to your right hand side them shadows get smaller and smaller untill early/mid summer and then longer and wider untill mid/late winter

The furthure away you are from the "tree line" the lower to the ground the balcony can be depending on actuall height of the tree(s). Which brings up the words height and stairs your might get in better shape if you option for height but If you can get 30-40 feet away from the tree lines the lower the balcony can be.

An end Apt unit might be the better pick over a middle of the building apt unit depending on foot print/shape of building. In the event of a "muti building lay out" middle buildings end apts might be the better options with the some southern balcony sun exposure mentioned prior.

Second areas of better sun is height AKA "Stairway to Heaven" Depending on the height of them trees your talking third forth or even higher floor(s) which does help a bit on balcony sun exposure directions but not much help on grocery shopping day.

Roses in pots is one concern, Lilies in pots is anouther see also the proper forums for better advice and selection ideas for containers/pots... For your two favorite flowering plants.

Also concider a Rent to own ideas as a late support idea

Best of luck to you

As a Land Lord here in Boston. I WOULD JUMP AT THE CHANCE for a tenant to maintain the yard. Here in the city our yards are small.
Take a peek on Craig's List at apt wanted. Google the address if possible and make contact with the LL. Ask if the rent would negotable "THE FIRST YEAR" if you were to do the gardening. I say first year to give him a sense of your skill and you the true amount of time to garden.
Also he may not want to reduce the rent, then pay for materials. So work it out i.e. gas money for the lawn mower, mulch.
But if someone took that off my plate, I may not reduce the rent here ( we still have more people than apts) but I wouldn't be raising the rent.
Good luck