Some limited research turned up Jamaica but it’s really hard to have comprehensive data on this. I know this is a long shot but maybe some doper has this arcane knowledge at their fingertips.
By connectivity, I mean packet loss, bandwidth and latency. In that order. Packet loss affects videoconferencing, bandwidth is not a huge deal, 50Mbps or so should do it, and latency is the least important for work, though it will suck for some online games 
If you mean “US timezone” precisely, then there aren’t very many options: You’ve got Central America, the Bahamas, Cuba, Haiti, Jamaica, Colombia, Ecuador, and Peru (plus a small, low-population-density, part of Brazil). Most of South America and over half of the Caribbean are further east than the GMT-5 Zone (what the US calls “Eastern”).
This Wiki ranking of countries by fixed broadband internet speeds has Panama (which is on the same time as EST) as the highest-ranked of the countries in question. I understand that speed alone is not the only metric the OP is interested in, but I suppose other relevant metrics correlate with it.
Interesting additional data:
Chile looks promising.
Chile is on EST plus two hours. At least now, during Southern summer, with Chile on DST; during the Northern summer it should be on the same time as EST because EST moves forward one hour and Chilean time back one hour. So it meets the OP’s specifications during half of the year.
GMT-4 is close enough to GMT-5 to be ok so I would include those countries (and PR) too. Chile is fine too @Schnitte.
@md-2000 cool map! Other interesting places are Cancun, Mexico and Panama.
Isn’t that list mobile only?
It has several lists. If you scroll down you will see the one for fixed broadband.
Sorry-Thank you.