We have 10 days to see Monteverde, Arenal, and Manuel Antonio; is it better to fly into Liberia and out of San Jose?
That depends! If it is advantageous for you to fly into Liberia (for example, if flying into Liberia is less expensive for you overall, if doing so offers you a preferred flight schedule, or if you have something specific in mind that you wish to experience in the Liberia region soon after you arrive into the country), then yes, it would be slightly better to fly out of San Jose given that Manuel Antonio (the last destination you plan to visit before flying home) is geographically closer to San Jose than Liberia. We use the adverb slightly on purpose, however. Since the difference in drive time between Manuel Antonio and the SJO Airport (approximately 3 hours) and Manuel Antonio and the LIR Airport (approximately 4 hours and 45 minutes) is only 1 hour and 45 minutes, you may determine that the drive difference between the two routes is not overly significant. Since flying into one airport and flying out of another usually costs more than round-trip flights purchased to and from the same airport, if this is the case for the flights you are looking at, you may find that saving yourselves the extra 1-hour-and-45-minute drive is not worth the added flight expense.
If there is no advantage to you flying into Liberia (or better yet, if there is an advantage to you flying into San Jose), we would recommend planning to fly into and out of the SJO Airport. Why? Because drive times between both Monteverde and Arenal are approximately the same from the SJO Airport as they are from the LIR Airport. If you plan to visit Monteverde first (as your question suggests), the drive will take approximately 3 hours to get to Monteverde from the airport in Liberia, versus approximately 3 hours and 15 minutes to get to Monteverde from the airport in San Jose. In this case, you will likely agree that flying into and out of San Jose would be the smartest option, since flying into Liberia provides little benefit. And, as an added bonus, if you opt to fly into San Jose and travel to Monteverde from there, although you will still encounter some bumpy roads as you enter the Monteverde region from this direction, you will avoid the worst/slowest/bumpiest section of road that exists on the route between Monteverde and Liberia.
Read our related blog post: Driving Directions To The SJO Airport / Driving Directions From The SJO Airport
Read our related blog post: Driving Directions To The LIR Airport / Driving Directions From The LIR Airport
Read our related blog post: Which Costa Rica Airport Is The Best? Comparing Costa Rica’s San Jose (SJO) Airport And Liberia (LIR) Airport