Livistona is a large genus of fan palms from Australia and Asia. Most (all?) are single trunked, attractive palms, with smooth trunks. They are difficult to sort out taxanomically; many species are rare and little is known about their hardiness. Results in hardiness trials have not always been consistent, but here are some considerations for various species.
L. chinensis is the most common species, and is often available for very low prices in nurseries or in the houseplant section of hardware stores. It is leaf-hardy to about -6°C/21°F and the trunk is hardy to much lower temperatures. However it takes many years to recover from leaf damage and it really not suitable for any except the most sheltered areas of the Pacific Northwest. There is a successful planting of this species in downtown Vancouver, BC in a very protected spot. It is a very slow-growing palm as a rule, and even more so with our lack of summer heat.
L. australis is perhaps a better species to try in the Pacific Northwest; some say it is hardier than L. chinensis and some say a little less so. In any case it is much better suited to our climate because it grows about three times as fast, ultimately making a large palm, and can be quite vigorous in cool weather. It is not as easy to obtain though.
L. nitida 'Canarvon Gorge' is likely to be (more or less) the hardiest species so far known, being just a little hardier than L. chinensis and L. australis in most (but not all) trials. L. sp. 'Victoria River' is another one that is supposed to be very hardy. L. decipiens is more common than these, and is known to be a little less hardy than L. australis.
There are numerous other Australian Livistona species are not so well known, many of which are difficult to identify and named for the locale where they were discovered and collected. Of these, species from montane areas of eastern Australia such as the large, attractive L. fulva 'Blackdown Tablelands' are the best to try and may be more or less comparable in hardiness to L. australis. Species from hot interior Australia such as L. mariae are rare in cultivation and their hardiness limits are not known, but it is not out of the question that some of these other Livistonas might be worth trying.
There are also more Asian Livistonas, most of which are strictly tropical or subtropical and cold tender. L. saribus is a variable palm with two known forms, one with a pink stripe on the petiole, and one with all-green petioles. The all green one is somewhat hardy, having withstood temperatures down to -7°C/19°F in Florida and recovering.
Obviously it would be useless to try to rank their hardiness (many more species exist that I know nothing about). They are generally easy to grow, and the hardier ones should be tried in sheltered spots west of the Cascades, with some protection in cold winters. Livistona seed germinates easily with bottom heat.