I wouldn't feel safe going up on a 30 year old shuttle, just like I wouldn't feel safe driving a 30 year old car.
Feelings are subjective
A 70 year old car can be in better shape as a 10 year old car...
Safety does not basically depend on age. It depends on maintenance and updates.
The Shuttle was the best maintained flying machine in the world with many modern updates. And more than 30 years after its development it still remains the most advanced flying machine ever designed. No other plane does reach a velocity of 8 km/s within less than 9 minutes, enters the atmosphere at a velocity of about 7.6 km/s and performs a spot landing on the runway, unpowered. It did so flawlessly for 30 years, manned from its first to its last flight.
Neither the Challenger nor the Columbia disaster was caused by aging. Shuttle flights could have continued not just for years, but even for another decades, just like many properly maintained airplanes do fly for half a century and longer. I took a seat on an Antonov AN2 which was build in the 1950s. It did fly like a charm and it still flies. I often see it and especially hear it while cleaning the windows of my attic flat in the summer.
the Russians have been sending up non-reusable Soyuz capsules forever at a fraction of the cost and they have a much better safety record than the shuttles!
The comparison is invalid. Because Soyuz is not a multipurpose, reusable spaceplane, that can carry tons of payloads and return it to earth. You have to compare the Shutte with Buran, which shows the reality of operating such vehicles. It was not any different for Russia. One test flight, unmanned, and that's it. Too expensive (beside technological issues), especially during collapse of the UDSSR.
Russia does operate Soyuz at a fraction of the cost, just like SpaceX does it with their small system, or like a Cessna 172 at my local airport is operated for lower costs than any Boeing 737.
has the ISS really made any breakthroughs, or is that just another money pit?
It's a working example of an international mega project in space, and the biggest stepping stone for future missions. The empirical and technological value is higher than the one of Apollo I think. Apollo was a big and awesome show, but not really something special technologically. The special thing basically was to leave earth orbit manned, enter the orbit of another heavenly body and land on it. But nothing of that stuff beats the Shuttle and ISS technologically so far.
Setting up research outposts on the Moon and further exploring it is integral to us keeping a constant and sustainable presence in space.
I don't think so. Flying to the Moon and live there has only very little to do with flying to Mars an live there for example. It's completely different challenges while flying to the Moon actually is no real challenge in comparison. It's only 1.3 seconds / 2 days away. It has no atmosphere and differs to the surface of Mars. And flying to an asteroid is another different story. What we need for a constant and sustainable presence in space is what we already have: a constantly occupied space station. Next step should be Mars. The Moon might be interesting for future unmanned research with advanced robot technologies.