One afternoon, we returned to Puuhonua o Honaunau to make use of another budget-friendly feature: free beachside barbecue grills. Equipped with charcoal and utensils from Lucky Farm, and a cooler full of ingredients from local markets, we cooked up a feast of tombo tuna, mahi-mahi and corn on the cob (which we soaked in a tidal pool to dampen the husks).

Along with an octopus-and-cucumber kimchi and a few bottles of pale ale from the Kona Brewing Company, we spent about $20 — perhaps a quarter of what the same meal would cost in an up-island restaurant like Merriman’s in Waimea, where the ponzu-marinated mahi-mahi is $34.95. Plus, we got to watch the sun sink into the Pacific, turning the water cool and silver before plunging us into darkness.

Try as we did to visit all the island’s beaches, parks and inexpensive restaurants, we soon came to understand why it’s called the Big Island: it’s really big (almost the size of Connecticut). With limited time, we saw only the white, yellow and gray sand beaches — not the black or green ones; we lunched on rich kalua pork and poi at Super J’s ($7), but never found the time for loco moco, the Hawaiian comfort dish of hamburger, a fried egg and gravy over rice, at Kenny’s, on the east coast.

Saddest of all, we never made it to Volcanoes National Park. But we did join Arnaud and Stéphanie, a young French couple who’d lucked into the Coffee Barn, on an excursion to Mauna Kea, the 13,796-foot mountain that is Hawaii’s tallest.

After a brief stop at the golden beach at the Four Seasons resort — access to the shoreline is a much-disputed public right — we began our ascent in a 4 x 4 and watched the landscape change, first subtly to the grassy, temperate ranches where local cattle roam, then dramatically to the treeless moonscape of lava fields below Mauna Kea’s peak. Surrounded by the white domes of stellar observatories, we gazed out on a carpet of clouds below us, and once again the sun turned the sky crimson before disappearing, revealing the vast band of the Milky Way encircling us.

So much was left to do on the Big Island, but we had to depart — after all, what’s a Hawaiian vacation without a little island-hopping? Thanks to an explosion of low-cost airlines, it’s easy to bounce around cheaply: Our round-trip tickets to Kauai on Go! cost $118 each, including a discount simply for joining the frequent-flier program. That’s not much for what amounts to a trip in a time machine — from the youngest of the main Hawaiian islands to the oldest.

Where the Big Island is vast and spacious, its lava fields flowing gently to the sea, five-million-year-old Kauai is knotty and lush, with eroded spires of volcanic rock shooting up from dense jungles of palms and pines, bamboo and guava groves. Kauai was the setting for “Jurassic Park,” and in this prehistoric setting, it’s not hard to imagine a couple of raptors sunning themselves at your side on one of the soft, sandy beaches that circle virtually the entire island.