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If you have an internet connection where you are going, visit the site doyogawithme for an opportunity to take a class along with the online teacher. You can pick the style of yoga, level of intensity, and length of class that fits your schedule.
You can always do yoga without a mat. BUT the mat does add cushion AND cleanliness. Gaiam has a new product of lightweight and mats that are perfect for travel. I have been packing my yoga towel when I travel; I look forward to purchasing this mat and using it instead!
Check out the Gaiam Sol Bhakti Ultra-Light Yoga Mat (1mm) - it may be just what you need to take your yoga with you while you travel!