Air purifiers with HEPA filters can be very effective on a room-by-room basis. Be sure to size the air purifier correctly. The better units will effectively scrub the air in a large room (500-1000 square feet). Also, be sure to select a purifier that has active air movement - a fan system that pulls air from the room and forces it through a pre-filter and a HEPA filter.
Air purifiers are one item where you'll probably get what you pay for. Inexpensive units suffer from three main faults. They tend to be noisy, have small, easily clogged filters and lack sufficient air flow.
When budgeting for air purifiers remember that they require a fair amount of regular maintenance. Pre-filters and filters need to be replaced at stated intervals or will stop working properly.