Hostas with fragrant flowers are generally the most sun tolerant.
There's an old rule of thumb that hostas with yellow leaves can handle the sun the best, but that isn't very reliable. Many yellow hostas have thin leaf substance and burn easily.
Hostas with fragrant flowers are all descendants of Hosta plantaginea, which is native to sub-tropical China. It is the most heat tolerant and sun tolerant of all hostas, and passes on these characteristics to its sports and hybrids.
Most hostas will do fine with a couple hours of morning sun. It is the intense mid day and afternoon sun that is the hardest on them. The more sun a hosta receives, the more water it will need. Good soil and a layer of wood mulch will help.
The location of your garden can play a big role in how much sun hostas can handle. Georgia sun is not the same as Iowa sun! The further north you are located, the more sun hostas can take.
Keep in mind that blue varieties need shade from hot sun to hold their blue color the longest. They may not be the best option for sunnier areas.
Regardless of what variety you choose, any hosta that is not used to growing in the sun will likely burn when first planted. Keep newly planted hostas well watered, and the new leaves will be more acclimated to the sun. Don't be too quick to assume a new hosta won't do well in its new location. Let it get established (at least one full season) before making the decision.
Below are some hosta varieties that tolerate sunnier locations.