You could probably fix your neck and shoulder pain issues by changing the fit of your existing bike, but a nice new touring specific bike can also help, especially if you buy a frame size that is large enough for you to get a decent more upright fit. Others have already posted some good choices, I ride a LHT, but you may also consider the Kona Sutra. KONA BIKES | ROAD | SUTRA | Sutra

There are a lot of good choices, you just have to find the one you like. You also need to find one that fits you. I have a 56cm LHT but could easily fit on a 54. I went with the 56 since it allows me to get the handlebars even, or above the seat easily without a huge stack of spacers. Right now my bars are an inch above my seat. I can ride all day without neck or shoulder pain, but, if I alter the fit a slight bit, seat position, stem change, or lower bars, I can introduce neck or shoulder pain, all those things work together to make you comfortable, change one and it can affect another. I can go with lower bars, But I might have to use a shorter stem than when they are higher. It is all about fit.