I learnt on Corel Draw thanks to the idiots at my university, but have since switched to Illustrator. It's quite the learning curve, but once you do you will wonder how you ever put up with Corel Draw (though there are still a couple things I preferred in CorelDraw, but whatever).
Actually this isn' the case. At leats not as far as I can tell. Illlustrator attempts to open CDR files, but every single .cdr file I've thrown at it it has said it s an unknown format.
The way I got my corel drawings to illustrator is by exporting them in COREL as Illustrator files, and THEN opening the .ai files in Illustrator. Sometimes I got some weird colour combos and lost drop-shadows, but nothing too bad.
So my advice is open the .cdr file in Corel, then go to File > Export and choose Adobe Illustrator in the Format drop-down menu.