Hi Lexie...I'm not sure what a Cat Palm is, but I'm assuming it's some type of palm, right? LOL
Most palms do not like a lot of heat in winter. In fact, more often than not, palms growing in artificial heated rooms will attract Spider Mites.
You also use the term, "frequent watering".. Are you saying you tend to overwater plants? Remember, soil needs to dry between waterings..(most tropicals) Never overwater a plant, especially while growing indoors during winter months.
The largest of Peace Lily's,(Mauna Loa) is a beautiful plant and does well in bright light..flowers are huge.
I believe the Mauna is the one you mean..

Lexie, there are many types of plants to choose from, but 78F is a bit hot. Is this a definate temperature? Toni

I've had good luck with the larger cultivars of peace lily, personally -- I've had one for a few years, and it's been pretty reasonable. The smaller ones seem to have more issues with dry air. Palms and I aren't really speaking to each other anymore, and I wouldn't really recommend them, but it's not impossible. Lady palms (Rhapis excelsa) are supposed to be nice.

If you're set on a big plant for both spots, there are some larger Aglaonemas (Chinese evergreen) that are very nice, and Ags are generally tolerant of everything except cold and full sun.

I have a large Dieffenbachia that's been with me a while too, which I am very fond of: they're less patient than Aglaonemas, and need a bit more watering, but even so.

The Dracaenas -- D. fragrans (corn plant) and D. deremensis ('Warneckii,' 'Lemon-Lime,' 'Janet Craig') are all very tolerant of neglect and dry air, and some get to be big. Overwatering is a concern. More or less the same thing goes for snake plants (Sansevieria trifasciata).

I'm also a big fan of the long-leaf fig (Ficus binnendijkii), which I have found to be just fine with almost everything I've tried to do with it.

Yucca elephantipes and Zamioculcas zamiifolia can both deal with pretty long periods of neglect, though both are slow growers (ZZ more so than Yucca) and will rot if overwatered. The Yucca might prefer more light than you have in those spots, but they're very adaptable.

Bird of paradise (Strelitzia nicolae, S. reginae) are a lot easier than they're given credit for, and I have mine (all four of them) in a west window. Watering is trickier with small plants than with large. Probably not the best choice, but if you like them, it could work out.

Rubber plant (Ficus elastica) and fiddle-leaf fig (Ficus lyrata) are both nice plants. A little moody, perhaps, but pretty tolerant of neglect and dry air, and both are great-looking if they're well taken care of.

Schefflera actinophylla (umbrella tree) is also probably possible, but I'm hesitant to recommend those because they're so easily devoured by spider mites, especially in dry air.

Toni-
I'm not really sure what a Cat Palm is either... that's just what the pot said. To me, it looks like any old palm! I don't usually overwater, in fact just the opposite. (I've discovered that misting cures the need to fuss with my plants without damage) I even try to keep all terra cotta to help monitor moisture. But hubby loves the tropical plants, and I'm willing to water a little more if needed. Normally, I water when I notice a little bit of wiltiness.
Did I say 78? I meant 75... and only at the warmest. I'd guess normally about 73.

Mr S-
WOW, thanks for all the suggestions!! I would like to have something a little larger since we have so much blank white wall space, and no plant stands! My regular peace lily is my largest, and is finally looking proportionate to its 12" pot.

"Cat palm" is the new old slang for Chamaedorea cataractum, a relative of the parlor palm (C. elegans) that was popular in the 70s. It is supposed to be even more attractive to spider mites than C. elegans is, if you can believe it.

Since the cat palm revival seems to have sprung up all at once, pretty recently, I'm thinking that someone may have bred or tissue-cultured or engineered a more pest-resistant variety, but I'm just guessing.

The giant peace lilies are one of my favorites - I like the tropical look that the large leaves give. The care is basically the same as for any other peace lily, but they do need larger quantities of water to support all that leaf area. One of my coworkers used to joke that they were a "peace lily with a drinking problem"! So if you get too busy to water, you could be in trouble. Do not put a peace lily right in front of a west window - it will bleach out and look icky. It should like your east window very much.

I don't recommend palms for most folks indoors - they are quite challenging, especially in conditions of warm, dry air that encourage spider mites. However, the lady palm (Rhapis excelsa) is a lot more tolerant than other types of palms. It would do well in your west window (that's where I have mine). You are unlikely to find one at Home Depot or Walmart, since they tend to be rather expensive.

mr subjunctive has some other excellent recommendations for you - you can probably find the rubber tree, some of the dracaenas (especially the corn plant), and some ficus at your Walmart or Home Depot. A ficus would love your west window - go for the long-leafed variety like Ficus alii if you can find it, although Ficus benjamina (the one usually seen) would do well too, it just drops leaves more often.

Lexie, Mr Sub and Watergal have given great advice.
Where do you plan on shopping?
I've 2 ideas.
Do you have plant books? Or is there a nearby library you can borrow plant books? If you can get your hands on a few, browse through pics and care..If you see a plant you like, read care instructions..If your rooms are suitable after reading care instructions, write down the name of plants, then start hunting for the plants you've jotted down.
Another idea is to go to your local nurseries, see what's available..If you don't mind starting smaller plants, you can find numerous places online. If you want large trees, go to local nurseries, or places like Home Depot, Lowe's (I never shopped there,) Ikea, Walmart and Menards. It's a good time to find tropicals since many are on sale..Most stores are trying to rid summer stock, you'd be shocked by their prices.
Walmart had a Red Cardinal Philodendron for 7.99 in a 10" pot..they're quite pretty, and grow tall. Lots of red on leaves/stems.
I too love the large leaf Peace Lily..it looks terrific in its own area..they grow wide and tall, w/huge leaves and flowers and don't require a ton of care..As long as it's not overwatered, gets at least medium sun, and fertilized twice a yr during growing season, you'll have a nice specimen. Let us know what you choose..Toni