Should I send a check to the IRS in order to pay my federal taxes since Im spending sometime out of the USA?

You can send a check or you can make the same payment online at IRS website - (online payment is easiest)

https://www.irs.gov/payments

If you want to send a check, you can use this voucher to send with your check -

https://www.irs.gov/pub/irs-pdf/f1040v.pdf