In the US, hospitals that serve as the primary clinical site for a MEDICAL
school are designated as "teaching hospitals". Please note that this designation has NO correlation with hospitals that provide Nursing or allied health clinical practicums, although these programs may also be present also. Since those hospitals derive significant (financial, marketing & possibly research) benefit from their medical school association, administrative decisions and operations are heavily influenced by this 'partnership'..... pretty much everything is designed to keep the med school happy. Although it is not a simple 'either/or' proposition, this type of environment is not one that automatically results in a strong and positive environment for nursing practice. So - "Teaching hospital" does not indicate a positive environment for nursing practice.
Formal new-grad transition programs are expensive, but they are certainly not limited to teaching hospitals - they can be found in any type of organization that can afford to have one. Please keep an open mind as you do your job search
. If a facility hires new grads, they will have some sort of process intended to provide support for them. The process may be individualized rather than group-oriented so they may not have a formal program. There are advantages to each. For instance, in a formal program you have access to peer support from other new grads in the group but in an individualized orientation, you would receive more one-on-one support and are less likely to have to deal with multiple preceptors. You can always discuss this as part of the interview process.
Congratulations on being so close to crossing that important graduation milestone. Best of luck on launching your career!