Relocating abroad, whether for a new job, higher education, or joining family, is exactly the kind of major life transition families like to time with a muhurat. Since your actual flight or visa dates are rarely flexible enough for a single “best day,” this works better as a set of favorable windows to fit your booking into.
Favorable windows in general
Traditionally, Shukla Paksha tithis (Dwitiya, Tritiya, Panchami, Saptami, Dashami, Ekadashi) and Wednesday, Thursday or Friday are considered favorable for starting a new chapter such as travel or relocation. Chaturmas (roughly July through November) and Malmas (the month the Sun transits Dhanu or Meena rashi, varying each year) are traditionally avoided for major beginnings.
Fit your travel date into the window
If your flight or visa appointment has some flexibility (a few days either way), check whether any of those days fall on a favorable tithi and weekday using the panchang page.
Checking the day-of timing
Once you have a candidate date, check that day’s Rahu Kaal and Abhijit Muhurat for your departure city on the muhurat page, and try to schedule the actual departure outside Rahu Kaal if possible.
This information is descriptive.