All of these flowers, if properly cut and maintained, should last well over a week, possibly over two weeks. Here are some of my favorite long-lived blossoms:
Gerbera daisies (below) look great, bunched or singly displayed in bud vases. Sometimes they are sold with a very thin wire snaking up their long, slightly furry stems. Leave the wire in place; it helps hold up their big, fat blooms.
Oriental lilies aren't cheap (you can see in this photo, below, they are priced at $4 per stem). But they are extravagantly beautiful, and even one stem will give you quite a show as the pods continue to split open and reveal beautiful blossoms for days on end.
Sunflowers just have to be some of the happiest-looking flowers on earth! Those sunny yellow petals, that big, friendly face! These chunky blooms with their thick stems won't fit in a slender bud vase and will look silly if you plop them in a coffee cup. So give them something tall and sturdy to stay in, like a pitcher or a glass carafe (the kind inexpensive house wine comes in at your neighborhood Italian restaurant).
Dianthus, or Sweet William, and I were introduced to each other at my neighborhood farmer's market. Related to carnations and to pinks, Dianthus sports multiple little flowers that make a big total impact. I bought this bouquet two weeks ago when I took this photo, and the flowers still look great.
Lastly, if you live anywhere near a Trader Joe's, run over there, fast! They are having their annual Daffodil sale, and a bunch of 10 happy daffodils is selling for the ridiculously low price of $1.29! That's a lotta flowers for very little cash, people! Because I haven't learned how to embed the link into the words "Trader Joe's" yet, here is the link: http://www.traderjoes.com/
And as with all produce, look at their labels (or ask the friendly flower seller at the farmer's market) to learn where the flowers came from. If it's a choice between Alstromeria (another long-lasting bloom!) grown in Peru and some grown just outside your city, please choose the local flowers. Mother Earth will thank you.