If it's causing you as much stress as it sounds like, it might be worth considering the option of finding transportation just for that drop-off job. One option is to ask a friend to drive you - just make sure it's not multiple times, or way too far, and try to do something nice for them soon after to show you appreciate it. Alternatively, you can rent a car or even cab it.
Whichever, try to make sure you've done as much as possible out of your sorting before this drop-off round, so you don't end up with more stuff to donate all the time.
Thereafter, it might be a good idea to designate an area of the basement as the 'donation corner', where you will put a box or something like that to toss things you no longer need for disposal about once a quarter. If that spot is the same, and the stuff stays corralled in a box out of sight, I bet you end up not noticing as much as you do now. You would need to do that anyway, because even if you've decluttered quite thoroughly, things still get the boot; I've tossed stuff because a better quality or more versatile version comes along, and I have no reason to deprive myself of that, so the older version gets passed along (btw this is one reason why I am always going on about how I don't see how decluttering and frugality are sometimes lumped together!)
Picking a spot by the front door is not a good place for most people for this long-term 'donatables corner' because it really does get in your line of sight multiple times a day. The basement sounds ideal, especially if it is mainly a storage space rather than a game room or TV room or gym and the like.
