If Garfield hadn't been assassinated, civil service reform might be somewhat delayed--although even the *attempt* at an assassination might be a stimulus for reform. As in OTL, the 1884 presidential election would be very close (the parties being very closely balanced between 1874 and 1894), but I rather doubt Garfield could win a second consecutive term--nobody between Grant and McKinley was able to do so. If Grover Cleveland wins the 1884 election, it's hard to see any long-lasting effects of Garfield having survived, except "butterfly" ones.
One possibility: Maybe President Garfield and his expansion-minded Secretary of State Blaine acquire Mole St. Nicolas, an excellent anchorage commanding the Windward Passage between Haiti and Cuba, from Haiti--something President Arthur and Secretary of State Frelinghuysen were not interested in doing.
https://groups.google.com/d/msg/soc.history.what-if/dfM2NaLg6Xo/NKy4MhY2H1oJ If the US had obtained the Mole, would it have found it necessary to get Guantanamo Bay after the Spanish-American War? After all, it would seem that the Windward Passage could be as easily commanded from the East as from the West. And without Guantanamo, US-Cuban relations might have been significantly different...