Sure, I'd be happy to assist with your travel plans.

Best Time to Visit:
Orléans, Bourges, Clermont-Ferrand, and Limoges have fairly mild weather year-round. The best time to visit would be from late spring to early autumn, particularly from May through September. This is when you can best enjoy their outdoor attractions.

Route and Accessibility:
All these cities are well connected by France's excellent train network. Starting point can be Paris if you're flying internationally. From Paris, you can reach Orléans in 1 hour by train, then Bourges by train in 1 hour and a half, Clermont-Ferrand in 2 hours, and Limoges in 2 hours from Bourges.

Altitude and Acclimatization:
These cities aren't at high altitudes, so no special acclimatization procedure is necessary.

Accommodation and Booking:
There are always plenty of hotels and accommodations available in these cities. However, it's best to book in advance to secure a good price and to ensure availability, especially in peak season.

Clothing and Essentials:
Pack comfortable shoes for walking around during your city tours. For clothing, pack based on the time of year you're travelling (light clothing for summer and warmer wear for autumn). Don’t forget your travel adapters for any electronic devices you plan to bring.

Health and Safety:
These cities are generally safe, but like any place, still watch out for personal belongings. Also carry personal medication if any, since brand names may vary by country.

Local Etiquette and Respect:
French people appreciate an attempt to communicate in French, even if it's just basic phrases. Tipping is also appreciated in restaurants, with it typically being around 5-10% of your total bill.