You can check with Melinh Plaza in Hanoi. They have various outdoor items and furniture, both local and imported.

Or if you're feeling particularly cheap, you can go to Quang Trung St by Lenin Park, where they sell lots of rattan furniture. You can get chairs, little tables, etc. They tend to smell a bit and aren't great for inside but are perfect for outdoor furniture that you don't care much about.

Melinh Plaza is at Thang Long- Noibai Kilometer 8th Highway. It is on the way to Noibai Airport, a bit far from the center of HN.

Besides, you could check with Sing Viet Furniture at 31 Ham Long St or go to Cat Linh Street, there are 2 big funiture shops and many small shop selling decorative things for outdoor.

Can's Rattan has nice teak outdoor tables & chairs, parasols. Cheap too. Near bottom left hand side of Lenin Park, 4 Nguyen Dinh Chieu Tel 9762246.