The one that will resonate with most is that you will save money. Travelers will find multiplied options for places to stay, larger budgets for special excursions, and the ability to splurge on some fine dining. Airfare and hotels can be as much as half off (though this also requires efficient planning and research), and knowing the window of dates that make up shoulder season can significantly ease the planning process.
One of my favorite perks of shoulder season is avoiding the crowds. This can mean shorter lines at the amusement park, less shoulder rubbing in the metro, securing an elusive last minute reservation at a popular restaurant, or spending time chatting with locals as they are not scrambling to entertain the massive wave of tourists during peak season.
With that said, here are a few tips for booking the right trip.
Evaluate your priorities. Peak season is such for a reason. How about Napa Valley? Do you want to go during the peak harvest season or in shoulder months where you might chat at length with a local winery owner? Advantages to both depending on priority, but the cost will not even be close. If your dream trip means paying the big bucks though, just do it and budget accordingly.
Be flexible. We planned last year to go to Spain in early May when the weather gets warm, instead, we went in mid March. Cost was about $1,000 less per person while staying at hotels we could not have afforded otherwise. Sure, our wardrobe was pants and a light jacket in the evenings, but it never rained and those savings have already paid for two other trips this year. Nothing we did in March differed from options available in May.
Do your research. It can be as simple as Googling "Where are the best places to travel in (fill in location) in September/October." Seems basic, but it can open up numerous new ideas. Check monthly averages for temp since fall may bring a larger swing from beginning to the end of the month (that can just mean a few more outfits to prepare for cooler nights, rain, etc.). Finally, look into hours and schedules of places you want to see. While prime attractions should still be available, there is a chance of some limited options.
Understanding shoulder season can be the difference in traveling or not, staying extra nights, or taking another full trip! There is an incredible array of places to go if you look in the right spots and have some flexibility. I might even help with the research part if you ask nicely :)
Note: shoulder season is not the cheap, cheap prices of low season. There is a reason rates are cut so drastically for some locations, and I would not necessarily recommend a lot of locations at low season.