But if you're talking about sites as in historic sites, then Long Wharf is closer to those (e.g., the Freedom Trail). Copley properties are indeed closer to the trendy Back Bay areas, but that is mostly commercial. There is some history stuff around Copley, but not as much as near LW. That said, downtown Boston is compact and none of these areas are far apart. It's less than one mile from the LW to Copley. So, if you're preferring what Dr. HDH lists, then Copley is ideal. If it's historic sites, then the LW is ideal. But either one will work well just because nothing downtown is particularly far from anyplace else. Even the oddly located RC is just a block off the Public Garden, which is a nice place for an afternoon walk.
The one thing about Boston, except for the most frigid of nights, people are out and about. If you let the weather severely impact your living, Boston is a terrible place to call home. I've been away for 15 years now and still miss it terribly - terrible weather and all. Remember to use the T. It's old and rickety, but exceptionally convenient and warmer than walking on cold nights.