Why did Jesus perform all his miracles among the nation of Israel?
Jesus performed His miracles among the nation of Israel to prove He was the promised Messiah, the King, ready to give them the kingdom, and to be their Redeemer. This confirmed His identity to Israel, not to Gentiles at that time.
Les explains that Jesus came to the nation of Israel and performed all these signs and wonders and miracles to prove He was that promised Messiah, the King, ready to give them the kingdom, as well as to be their Redeemer. The context shows Peter addressing 'Ye men of Israel' at Pentecost, with nothing concerning the Gentiles. David's prophecies were not yet about the salvation of Gentiles, but only that everything could be fulfilled so He could be Israel's Redeemer, and Israel could pass it out to surrounding nations and be priests.
Ye men of Israel, hear these words; Jesus of Nazareth, a man approved of God among you by miracles and wonders and signs, which God did by him in the midst of you, as ye yourselves also know: