Day trips from New York on the Metro-North train

Whom to bring: Antique lovers with a penchant for grand old estates
What to do: Stop sniffing out the next best thing on Twitter and look back in time instead, courtesy of this charming Westchester, NY village 25 miles from our fair metropolis. Historic mansions abound, but we like Kykuit (381 N Broadway at Pocantico St, Sleepy Hollow; hudsonvalley.org), the six-story manor that housed four generations of Rockefellers and is an easy five-minute cab ride from the train station ($4–$6). Stately architecture, elaborate gardens, Andy Warhol silkscreens and Picasso tapestries—there’s a lot to explore within this landmark estate. Once you’re green with envy, head back into town for a little retro shopping at Tarrytown’s numerous antique shops, such as Carol Master Antiques (10 Main St between N Broadway and Kaldenberg Pl, 914-332-8441).
Where to eat: Do as the locals do and lunch at Lefteris Gyro (1 N Broadway at Main St, 914-524-9687), which rolls out authentic Greek standards at wallet-friendly prices. Save room for dessert: Main Street Sweets (35 N Main St at Washington St, 914-332-5757) offers scoops of homemade ice cream in decadent flavors such as fudge-laced mocha.
How to get there: Take the Hudson line to Tarrytown station (35mins, Kykuit Tour $40, includes round-trip and Classic Tour; mta.info/mnr).

(Bear Mountain, NY; 845-786-2701, nysparks.com)

Whom to bring: A jaded city mouse who desperately needs a head-clearing nature fix
What to do: There’s a hike for everyone among Bear Mountain’s tranquil, woodsy trails, from the short loop around Brooks Lake to the more challenging four-mile segment of the Appalachian Trail. Most impressive is the steep, twisting trek to the Perkins Memorial Tower, from where you’ll have a stunning 360-degree vista of four states (NY, NJ, CT and PA), the Big Apple skyline, Storm King Art Center, the Hudson Highlands and the Hudson River some 1,000 feet below. If you’ve got any juice left after your climb, shoot hoops at the on-site basketball courts.
Where to eat: BYO picnic, as food options are limited in the park’s immediate vicinity. If you’re really in a pinch, the café–gift shop at the Bear Mountain Inn (55 Hessian Dr, 845-786-2731) sells overpriced necessities.
How to get there: Take the Hudson line to Peekskill station (45mins, round-trip $21.50–$28.50) and then a 15-minute cab ride to Bear Mountain (around $20).

(3 Beekman St between W Main and River Sts, Beacon, NY; 845-440-0100, diaart.org)

Whom to bring: An art buff who’s no longer impressed by MoMA—or any other museum in town
What to do: You can easily spend a whole day exploring the Dia Art Foundation’s extensive, A-list art collection. In the luminous, hangarlike former Nabisco factory, you’ll encounter large-scale works dating from the 1960s to the present. They include pieces by Andy Warhol, Louise Bourgeois and Richard Serra—namely his fantastical quartet of towering rolled-steel sculptures, Torqued Ellipses. Through the end of 2012, check out Parisian artist Jean-Luc Moulène’s debut solo U.S. exhibition of abstract objects and urban photo suites, Opus + One. Check the website before you visit, as museum hours vary seasonally.
Where to eat: Stroll past galleries and antique shops on Beacon’s quaint Main Street and grab a bite at the Hop (458 Main St between Schenck and Tioronda Aves, thehopbeacon.com), an unpretentious bistro that serves craft beer and artisanal small plates, such as rabbit-and-raisin terrine ($13).
How to get there: Take the Hudson line to Beacon station (70mins; One-Day Getaway Package $31.50, includes round-trip and museum admission) and walk five minutes to the museum.