Q&A: Northern Light for Indoor Trees
Q: What kind of indoor tree will thrive near a window with a northern exposure?

A: That's a tough situation. The best plants for such a spot tolerate low light: the bamboo palm or lady palm (Rhapis excelsa), a shrubby palm that can reach 10 feet tall; or the corn plant (Dracaena fragrans), a slow-growing upright shrub that indoors may get five to eight feet tall, but outside in sub-tropical climates, a 20-foot tree. The tree philodendron (P. bipinnatifidum) could be an option because it can tolerate low light, but its eventual girth (as wide as tall) could overwhelm a room. Indoors, it typically achieves seven feet high and wide and requires staking.
Some medium-light plants are occasionally known to tolerate lower-light conditions.Schefflera arboricola (schefflera, Australian umbrella tree) is shrubby but it can reach about seven feet and handle low light. You might try banana-leaf fig (Ficus maclellandii); it tends to need medium light but it may adjust to less light. It's a slow grower but can eventually reach 10 feet tall.
Lastly, for still more choices, consider one of the shrubby plants that love low light, such as the Chinese evergreen (Aglaonema) or the parlor palm (Chamaedorea elegans). Put one of these on an attractive plant stand, and you've got the height you want. Hope these ideas help!