A relatively inexpensive gift idea would be an antique signet ring with some special letters (maybe a,e,o) or your name engraved on the inside with your Big's initials on the signet. Gold antique signet rings can be found in the $15-$35 range on ebay. My jeweler charges around $10 for engraving.
If I am remembering correctly, Alpha Phi does not have an "official jewel"??? If Alpha Phi has an offical jewel, then a simple ring with the jewel or the jewel surrounded by diamonds is also a nice gift.
Another option that is even less expensive, but VERY memorable, is to find an antique sterling silver ($10-$30) or silverplated (50 cents-$20) large serving piece at a fleamarket or on an Internet auction site. Some of the early patterns had ivy on the handles; and most early patterns had space for engraving on the handle. Have the large serving piece engraved with Alpha Phi. It will be treasured.
On a related note....I have a silver serving piece that my husband gave to me YEARS before I was initiated into AOII. Imagine my SHOCK when I found my new letters engraved on the handle!
Let us know what you decide for a gift!

Silver