The Hebrew word is "mesillot", meaning "highway". The context of the Psalm is talking about going up to Jerusalem:
Psa. 84:4 Blessed are those who dwell in Your house;
They will still be praising You.
Psa. 84:7 They go from strength to strength;
Each one appears before God in Zion.
Moreover, the LXX translates the verse,
Psa. 83:5 Blessed is the man whose help is of thee, O Lord; in his heart he has purposed to go up
Thus the LXX understands the verse to be using the word "highway" in the sense of travelling on a highway toward Jerusalem" (that is, "going up", a common expression for ascending the hill toward Jerusalem).
The NKJV agrees with the NIV and NLT about using the word "pilgrimage", referring to the annual feasts to which all families in Israel were invited. The ESV and NASB, though using the word "highway" in translation, add "to Zion" so the reader will understand that it is the travel toward Jerusalem to which the Psalmist refers. Very few translations follow the KJV in understanding "ways" to be referring to God's ways.