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If you've recently upgraded to General, you might be looking for a good way to learn about operating on the HF bands. My introduction was a "worked-all-states" net, where people from around the country check in, make contacts, and start their QSL card collections. The clubs have awards, and you can also work toward the ARRL's "Worked All States" award. More importantly, you learn about propagation and how the bands behave in a painless environment. The club I joined is the 3905 Century Club (www.3905ccn.com) where I serve as Net Control on the Sunday night 75 meter net, but there are others as well.
You might also look into contesting. (Spoiler alert: you're not going to win. So relax.) My first contest was the ARRL Sweepstakes, which gives you hundreds of opportunities to work the US and Canada. You can set realistic goals for yourself like one contact in each state, or one contact in each ARRL section, or just a better score than last year. For more information, find the contest website and read the rules. Then just dive in! As always, you can ask around the club and you'll find someone who can give you advice. If you really catch the contesting bug, there are clubs nearby that specialize in contesting, like the Hudson Valley Contesters and DXers.