First, we need to talk terminology. What you are looking for is armor that gives you the effect of REFRESH. Regen deals with HP recovery only, Refresh deals with MP recovery and there is a difference when you are discussing and trying to research this type of info.
Next, there is a vast range of gear that you can get ranging from VERY expensive to the tried and true that is no longer expensive to items that will take questing, gathering items and risking life, limb and your very sanity to acquire - but who said any of us FFXI players were sane, huh? You can get the Wayfarer Robe Set, that in my opinion, is generic looking as hell, cheap in that you get it from the Records of Eminence A.M.A.N NPC by exchanging your Copper Vouchers by doing the daily "tasks" that are part of the Records of Eminence. But this set has got to be one of the most kick ass sets of level 99 gear I've seen in a long, long time for mages. You can wear it for WHM, RDM and BLM, but you have to wear all 5 pieces. Also, if you haven't participated in the Records of Eminence, get with the program and do it - it is well worth your time, trust me. There are weapons and gear that are so worth your time it isn't even funny.
Now if you want to get more specialized gear, the best place to start looking specifically at Refresh equipment is on the online FFXIAH.com. There is a search you can do that will pin point all the gear that has "Refresh" in it's description and then you can follow each piece over to FFXIclopedia.org and hopefully a page has been created for each item - not all items are updated since the database is maintained by volunteers and there is so much data and so much changes over times.
There are pieces that are specialized like the WHM ClericRelic gear, if you get the entire set, it has an effect of Refresh built in. But only a WHM can wear that set, of course. Also, there is the Noble Tunic, which I paid a couple of million for about 10 years ago. All you need is the Tunic, not the entire set. The Tunic goes for 30k now, IF you can find it at the AH, find someone to craft it for you or find someone to sell it to you. I know for a fact that I would never sell my Nobles, I'm too attached even though I never used it anymore. I wore that sucker for years and years on my WHM....oh, WHMs only can wear them.
Give this link a try to see if you can get my search results on the FFXIAH.com. If it doesn't work, so to FFXIAH.com. Where you see Item Search on the left hand side, first chose your server, then click "Power Search". In the Description box type in on the word Refresh (in researching, the less info you put in the better your results). On the right side of the page you will see Boxes that list Job, Race and Slot. In the Slot box, hold down your CTRL key and click on Head, Body, Hands, Legs and Feet. Then click SUBMIT.
You only have to do all of the above if the link below doesn't work. You can sort the link by Alpha and level. I suggest you do sort by level right away. The site has a weird habit of hiding everything that is 76 or higher. By clicking search it will pull in all the gear that is over level 75 to 99. Click on an item you want to look at and you will have a choice of 4 databases that you can link to for more info to check out the items. BTW if the item is listed at 0 price and Dead Slow that means that it is a quested Rare/EX item that is quested only and can't be bought on the AH - so get ready for your sanity to be tested.