JYSK is a Danish furniture franchise in Aeon mall and on Xuan Dieu, offering furniture and soft furnishings including bedding. UMA is an expat owned furniture store similar in style to IKEA. Another IKEA alternative is index living mall in Times City. For good quality heavy wooden furniture, you could try Grand Bois and Dome. Y-Not offers custom made furniture, as does the cheaper alternative Maroon Driftwood or Tropical Rustic.
For nice wooden tables and furniture rustic home is a good choice.
There are more and more companies coming to Hanoi with high-end furniture like BoConcept or Ligne Roset in Sun Grand Plaza (69 Thuy Khue).