I'm going to assume you mean 1st person games, where you are "looking through the eyes of your character" and not "seeing the character" onscreen while you play.
I don't know of many new ones, so you may already have played most of these...
Since you liked Return to Mysterious Island, you might check out other games developed by Kheops Studios (their list of games is available on the
***archive of their website***.
I'm not sure if you meant "Secrets of Da Vinci" or "Da Vinci Code." People confuse the names all the time because the name of the book is well known while "Secrets of..." is not. I have not played the game specifically called "Da Vinci Code," which
***Mobygames*** classifies as a 3rd person action game rather than an adventure.
But if it was "Secrets of Da Vinci" that you were thinking of, you'd probably also like "Nostradamus: The Last Prophecy" (also made by Kheops and very similar). Be warned that there are at least two "casual" games with Nostradamus in the title. Make sure you know what you're buying. Steam has Nostradamus
http://store.steampowered.com/app/287720/Some of the Kheops games are available at GOG.com but some have never been available there and some have been removed. I'll try to include a download link if I know of one. I usually use gog.com but have also bought from dotemu.com and shinyloot.com
Some Gameboomers members like Steam, Gamersgate, and Amazon. Amazon downloads often use Steam keys. If you buy from Big Fish, be aware that many of their older games have been "updated" by increasing graphics resolution but removing puzzles and interactive hotspots. It's something done by the company that "updated" the games rather than by Big Fish itself.
Baron Wittard
Gameplay is very similar to the Kheops games.
A few screenshots here
http://store.steampowered.com/app/293980/Kairo
Available from the game website
http://kairo.lockeddoorpuzzle.com/Atlantis 2 and 3, available for download at websites like GOG, Steam, DotEMU
http://www.gog.com/game/atlantis_2_beyond_atlantishttp://www.gog.com/game/atlantis_3_the_new_worldAtlantis 1 (The Lost Tales) has a lot of timed puzzles where you end up being killed or thrown in prison before you realize what you're supposed to do to get past an obstacle. So I wouldn't recommend it unless you don't mind that kind of thing.
The RHEM series
http://rhem-game.com/Low resolution 640x480 graphics, but the puzzles are excellent
Riven -- if you haven't already played it
http://www.gog.com/game/riven_the_sequel_to_mystAmerzone
http://www.gog.com/game/amerzone_the_explorer_legacyShivers and Shivers 2 (these are also older games, and I don't know of any stores that offer versions that run on modern computers. So you'd have to buy a physical version)
Shivers 2 has an installer for new computers.
http://squirtthecat.com/You may need an older computer to play Shivers on a modern computer, unless you install inside of DOSBox (with Windows 3.1) or inside a virtual machine like Virtual PC with Windows 95/98 installed.
Amber: Journey's Beyond
Another older game that has an installer at
http://squirtthecat.comZork Nemesis and Zork Grand Inquisitor
http://www.gog.com/game/zork_nemesis_the_forbidden_landshttp://www.gog.com/game/zork_grand_inquisitor(Zork Nemesis is a dark/creepy-style game, while Grand Inquisitor is a humorous game)
Journeyman Project 3
Another old one now sold as a download
http://www.gog.com/game/journeyman_project_3The other Journeyman Project games don't have a full screen game window. To see what I mean, check screenshots such as those at
http://www.gog.com/game/journeyman_project_2Dracula 1, 2, and 3
http://www.gog.com/game/dracula_trilogyYou can also buy Dracula 4 and 5, but they are short, more "casualized" and less immersive (IMO) than the first 3. Honestly I wouldn't recommend them unless you can get them half off the regular price.
http://www.gog.com/game/dracula_4_5==========================================================
Some modern games that aren't exactly the style of Return to Mysterious Island (not specifically 1st person) but have puzzles:
Lumino City
http://www.gog.com/game/lumino_cityBotanicula
http://www.gog.com/game/botaniculaMachinarium
http://www.gog.com/game/machinarium_collectors_edition(I don't know if they've fixed the bug where your saved game for Machinarium gets deleted if you use your browser and use cleanup software like is in ccleaner, some antimalware software, or the better privacy addon, but it wasn't fixed as of last year. Also, there is an arcade sequence near the end of the game I was never able to get past -- partly because my saved game disappeared due to the bug.)
Journey of a Roach
http://www.gog.com/game/journey_of_a_roachShort but cute -- the little bug must navigate environmental puzzles.
Gomo
http://www.gog.com/game/gomoSimilar to Journey of a Roach, only you play as a brown paper bag.
I'm sure I'm forgetting a few games, but there haven't been many first person puzzle-oriented games made recently. Modern first person games tend to lack puzzles. And you may have already played most of the older ones.